\newcommand{\etalchar}[1]{$^{#1}$}
\begin{thebibliography}{HLGOR94b}

\bibitem[Abb89]{Abb89}
J.~A. Abbott.
\newblock {\em On the Factorization of Polynomials over Algebraic Fields}.
\newblock PhD thesis, School of Mathematical Sciences, University of Bath,
  September 1989.

\bibitem[AMW82]{AMW82}
D[avid]~G. Arrell, S[anjiv] Manrai, and M[ichael]~F. Worboys.
\newblock A procedure for obtaining simplified defining relations for a
  subgroup.
\newblock In Campbell and Robertson \cite{GrpsStAndrews81}, pages 155--159.

\bibitem[AR84]{AR84}
D[avid]~G. Arrell and E[dmund]~F. Robertson.
\newblock A modified {T}odd-{C}oxeter algorithm.
\newblock In Atkinson \cite{Durham82}, pages 27--32.

\bibitem[Art68]{Art68}
E[mil] Artin.
\newblock {\em Galoissche Theorie}.
\newblock Verlag Harri Deutsch, Frankfurt/Main, 1968.

\bibitem[Atk84]{Durham82}
Michael~D. Atkinson, editor.
\newblock {\em Computational Group Theory, Proceedings LMS Symposium on
  Computational Group Theory, Durham 1982}. Academic Press, 1984.

\bibitem[Bau91]{Bau91}
Ulrich Baum.
\newblock {\em Existenz und effiziente {K}onstruktion schneller
  {F}ouriertransformationen {\accent127 u}beraufl{\accent127 o}sbarer
  {G}ruppen}.
\newblock Dissertation, Rheinische Friedrich Wilhelm Universit{\accent127 a}t
  Bonn, Bonn, Germany, 1991.

\bibitem[BBN{\etalchar{+}}78]{BBNWZ78}
Harold Brown, Rolf B{\accent127 u}low, Joachim Neub{\accent127 u}ser, Hans
  Wondratschek, and Hans Zassenhaus.
\newblock {\em Crystallographic Groups of Four-Dimensional Space}.
\newblock John Wiley, New York, 1978.

\bibitem[BC76]{BC76}
M[ichael]~J. Beetham and C[olin]~M. Campbell.
\newblock A note on the {T}odd-{C}oxeter coset enumeration algorithm.
\newblock {\em Proc. Edinburgh Math. Soc. (2)}, 20:73--79, 1976.

\bibitem[BC89]{BC89}
Richard~P. Brent and Graeme~L. Cohen.
\newblock A new lower bound for odd perfect numbers.
\newblock {\em Math. Comput.}, 53:431--437, 1989.

\bibitem[BC92]{BC92}
Wieb Bosma and John~[J.] Cannon.
\newblock Handbook of {Cayley} functions.
\newblock Technical report, Department of Pure Mathematics, University of
  Sydney, Sydney, Australia, 1992.

\bibitem[BCFS91]{BCFS91}
L[azlo] Babai, G[ene] Cooperman, L[arry] Finkelstein, and \'A[kos] Seress.
\newblock Nearly linear time algorithms for permutation groups with a small
  base.
\newblock In {\em Proceedings of the International Symposium on Symbolic and
  Algebraic Computation (ISSAC'91), Bonn 1991}, pages 200--209. ACM Press,
  1991.

\bibitem[BCN89]{BCN89}
A.E. Brouwer, A.M. Cohen, and A.~Neumaier.
\newblock {\em Distance-Regular Graphs}.
\newblock Spinger, Berlin and New York, 1989.

\bibitem[Ber76]{Ber76}
T.~R. Berger.
\newblock Characters and derived length in groups of odd order.
\newblock {\em J. Algebra}, 39:199--207, 1976.

\bibitem[Bis89]{Bis89}
Thomas Bischops.
\newblock Collectoren im {P}rogrammsystem {GAP}.
\newblock Diplomarbeit, Lehrstuhl D f{\accent127 u}r Mathematik, Rheinisch
  Westf{\accent127 a}lische Technische Hoch\-schule, Aachen, Germany, 1989.

\bibitem[BM83]{BM83}
Gregory Butler and John McKay.
\newblock The transitive groups of degree up to 11.
\newblock {\em Communications in Algebra}, 11:863--911, 1983.

\bibitem[Bra89]{Bra89}
R.~J. Bradford.
\newblock {\em On the computation of integral bases and defects of integrity}.
\newblock PhD thesis, School of Mathematical Sciences, University of Bath,
  1989.

\bibitem[BTW93]{BTW93}
Bernhard Beauzamy, Vilmar Trevisan, and Paul~S. Wang.
\newblock Polynomial factorization: Sharp bounds, {E}fficient algorithms.
\newblock {\em J. Symbolic Computation}, 15:393--413, 1993.

\bibitem[Bur55]{Bur55}
W[illiam~S.] Burnside.
\newblock {\em Theory of Groups of Finite Order}.
\newblock Dover Publications, New York, 1955.
\newblock Unabridged republication of the second edition, published in 1911.

\bibitem[But82]{But82}
Gregory Butler.
\newblock Computing in permutation and matrix groups {II}: Backtrack algorithm.
\newblock {\em Math. Comput.}, 39:671--680, 1982.

\bibitem[But85]{But85a}
Gregory Butler.
\newblock Effective computation with group homomorphisms.
\newblock {\em J. Symbolic Computation}, 1:143--157, 1985.

\bibitem[Cam71]{Cam71}
Harvey~A. Campbell.
\newblock An extension of coset enumeration.
\newblock M. {S}c. thesis, McGill University, Montreal, Canada, 1971.

\bibitem[CCN{\etalchar{+}}85]{CCN85}
J[ohn]~H. Conway, R[obert]~T. Curtis, S[imon]~P. Norton, R[ichard]~A. Parker,
  and R[obert]~A. Wilson.
\newblock {\em Atlas of finite groups}.
\newblock Oxford University Press, 1985.

\bibitem[Cel92]{Cel92}
Frank Celler.
\newblock Kohomologie und {N}ormalisatoren in {GAP}.
\newblock Diplomarbeit, Lehrstuhl D f{\accent127 u}r Mathematik, Rheinisch
  Westf{\accent127 a}lische Technische Hoch\-schule, Aachen, Germany, 1992.

\bibitem[CNW90]{CNW90}
Frank Celler, Joachim Neub{\accent127 u}ser, and Charles~R.~B. Wright.
\newblock Some remarks on the computation of complements and normalizers in
  soluble groups.
\newblock {\em Acta Applicandae Mathematicae}, 21:57--76, 1990.

\bibitem[Coh93]{Coh93}
Henri Cohen.
\newblock {\em A Course in Computational Algebraic Number Theory}, volume 138
  of {\em Graduate Texts in Mathematics}.
\newblock Spinger, Berlin and New York, 1993.

\bibitem[Con90a]{Con90a}
S[am]~B. Conlon.
\newblock Calculating characters of $p$-groups.
\newblock {\em J. Symbolic Computation}, 9(5 \& 6):535--550, 1990.

\bibitem[Con90b]{Con90b}
S[am]~B. Conlon.
\newblock Computing modular and projective character degrees of soluble groups.
\newblock {\em J. Symbolic Computation}, 9(5 \& 6):551--570, 1990.

\bibitem[CR82]{GrpsStAndrews81}
Colin~M. Campbell and Edmund~F. Robertson, editors.
\newblock {\em Groups-St.\,Andrews 1981, Proceedings of a conference,
  St.\,Andrews 1981}, LMS Lecture Note Series, vol. 71. Cambridge University
  Press, 1982.

\bibitem[Dix67]{Dix67}
J[ohn]~D. Dixon.
\newblock High speed computations of group characters.
\newblock {\em Num. Math.}, 10:446--450, 1967.

\bibitem[Dre69]{Dre69}
Andreas [W.~M.] Dress.
\newblock A characterization of solvable groups.
\newblock {\em Math. Z.}, 110:213--217, 1969.

\bibitem[FJNT]{FJNT93}
V[olkmar] Felsch, D[avid]~L. Johnson, J[oachim] Neub{\accent127 u}ser, and
  S[ergey]~V. Tsaranov.
\newblock The structure of certain {C}oxeter groups.
\newblock To appear.

\bibitem[Fra82]{Fra82}
J[ames]~S. Frame.
\newblock Recursive computation of tensor power components.
\newblock {\em Bay\-reu\-ther Math. Schr.}, 10:153--159, 1982.

\bibitem[FS84]{FS84}
Volkmar Felsch and G{\accent127 u}nter Sandl{\accent127 o}bes.
\newblock An interactive program for computing subgroups.
\newblock In Atkinson \cite{Durham82}, pages 137--143.

\bibitem[GKP90]{GKP90}
Ronald~L. Graham, Donald~E. Knuth, and Oren Patashnik.
\newblock {\em Concrete Mathematics}.
\newblock Addison-Wesley, 1990.

\bibitem[Gla87]{Gla87}
S[tephan]~P. Glasby.
\newblock {\em Computational Approaches to the Theory of Finite Soluble
  Groups}.
\newblock Phd thesis, Department of Pure Mathematics, University of Sydney,
  Sydney, Australia, 1987.

\bibitem[GS90]{GS90}
S[tephan]~P. Glasby and M[ichael]~C. Slattery.
\newblock Computing intersections and normalizers in soluble groups.
\newblock {\em J. Symbolic Computation}, 9:637--651, 1990.

\bibitem[Hah83]{Hah83}
Theo Hahn, editor.
\newblock {\em International Tables for Crystallography, Volume A, Space-group
  Symmetry}.
\newblock Reidel, Dordrecht, Boston, 1983.

\bibitem[Hav69]{Hav69}
George Havas.
\newblock Symbolic and algebraic calculation.
\newblock Basser Computing Dept., Technical Report~89, Basser Department of
  Computer Science, University of Sydney, Sydney, Australia, 1969.

\bibitem[Hav74]{Hav74b}
George Havas.
\newblock A {R}eidemeister-{S}chreier program.
\newblock In M[ichael]~F. Newman, editor, {\em Proceedings of the Second
  International Conference on the Theory of Groups, Canberra, 1973}, Lecture
  Notes in Mathematics, vol. 372, pages 347--356. Springer, Berlin, 1974.

\bibitem[HI{\accent127 O}89]{HIO89}
Trevor~[O.] Hawkes, I.~M[artin] Isaacs, and M.~{\accent127 O}zaydin.
\newblock On the {M\accent127 o}bius function of a finite group.
\newblock {\em Rocky Mountain J. Math.}, 19:1003--1034, 1989.

\bibitem[HKRR84]{HKRR84}
George Havas, P[eter]~E. Kenne, J[ames]~S. Richardson, and E[dmund]~F.
  Robertson.
\newblock A {T}ietze transformation program.
\newblock In Atkinson \cite{Durham82}, pages 67--71.

\bibitem[HLGOR94a]{HLOR94a}
Derek~[F.] Holt, Charles~[R.] Leedham-Green, E[amonn]~A. O{\accent19{}B}rien,
  and Sarah Rees.
\newblock Computing matrix group decompositions with respect to a normal
  subgroup.
\newblock submitted to London Math. Soc., 1994.

\bibitem[HLGOR94b]{HLOR94b}
Derek~[F.] Holt, Charles~[R.] Leedham-Green, E[amonn]~A. O{\accent19{}B}rien,
  and Sarah Rees.
\newblock Primitivity testing for matrix groups.
\newblock submitted to London Math. Soc., 1994.

\bibitem[HN80]{HN80}
George Havas and M[ichael]~F. Newman.
\newblock Application of computers to questions like those of {Burnside}.
\newblock In J[ens]~L. Mennicke, editor, {\em Burnside groups, Proceedings of a
  workshop, Bielefeld, Germany, 1977}, Lecture notes in Mathematics, vol. 806,
  pages 211--230. Springer, Berlin, 1980.

\bibitem[HR94]{HR94}
Derek~[F.] Holt and Sarah Rees.
\newblock Testing modules for irreducibility.
\newblock {\em J. Austral. Math. Soc. Ser. A}, 57, 1994.

\bibitem[HS64]{HS64}
Marshall Hall, Jr. and James~K. Senior.
\newblock {\em The Groups of Order $2^n$ ($n \le 6$)}.
\newblock The Macmillan Company, New York, 1964.

\bibitem[Hup67]{Hup67}
B[ertram] Huppert.
\newblock {\em Endliche {Gruppen} {I}}, volume 134 of {\em Grundlehren Math.
  Wiss.}
\newblock Springer, Berlin, 1967.

\bibitem[Ker91]{Ker91}
Adalbert Kerber.
\newblock {\em Algebraic Combinatorics Via Finite Group Actions}.
\newblock BI-Wis\-sen\-schafts\-ver\-lag, Mannheim, 1991.

\bibitem[Lau82]{Lau82}
Reinhard Laue.
\newblock {\em Zur {Konstruktion} und {Klassifikation} endlicher
  aufl{\accent127 o}sbarer {Gruppen}}, volume~9 of {\em Bay\-reu\-ther Math.
  Schr.}
\newblock Universit{\accent127 a}t Bayreuth, Bayreuth, Germany, 1982.

\bibitem[Leh89a]{Sog89}
Lehrstuhl D f{\accent127 u}r Mathematik, Rheinisch Westf{\accent127 a}lische
  Technische Hoch\-schule, Aachen, Germany.
\newblock {\em {SOGOS} - A Program System for Handling Subgroups of Finite
  Soluble Groups, version 5.0, User's reference manual}, 1989.

\bibitem[Leh89b]{Spa89}
Lehrstuhl D f{\accent127 u}r Mathematik, Rheinisch Westf{\accent127 a}lische
  Technische Hoch\-schule, Aachen, Germany.
\newblock {\em {SPAS} - {S}ubgroup {P}resentation {A}lgorithms {S}ystem,
  version 2.5, User's reference manual}, 1989.

\bibitem[Leo80]{Leo80}
Jeffrey~S. Leon.
\newblock On an algorithm for finding a base and a strong generating set for a
  group given by generating permutations.
\newblock {\em Math. Comput.}, 35:941--974, 1980.

\bibitem[LGS90]{LS90}
C[harles]~R. Leedham-Green and L[eonard]~H. Soicher.
\newblock Collection from the left and other strategies.
\newblock {\em J. Symbolic Computation}, 9(5 \& 6):665--675, 1990.

\bibitem[Lin93]{Lin93}
Steve Linton.
\newblock {\em Vector Enumeration Programs, version 3}, 1993.

\bibitem[LLL82]{LLL82}
A.~K. Lenstra, H.~W. Lenstra, and L.~Lov{\accent19 a}sz.
\newblock Factoring polynomials with rational coefficients.
\newblock {\em Math. Ann.}, 261:513--534, 1982.

\bibitem[LNS84]{LNS84}
R[einhard] Laue, J[oachim] Neub{\accent127 u}ser, and U[lrich] Schoenwaelder.
\newblock Algorithms for finite soluble groups and the {SOGOS} system.
\newblock In Atkinson \cite{Durham82}, pages 105--135.

\bibitem[LP91]{LP91}
Klaus Lux and Herbert Pahlings.
\newblock Computational aspects of representation theory of finite groups.
\newblock In G.~O. Michler and C.~R. Ringel, editors, {\em Representation
  theory of finite groups and finite--dimensional algebras}, volume~95 of {\em
  Progress in Mathematics}, pages 37--64. Birkh{\accent127 a}user, Basel, 1991.

\bibitem[LPW93]{LPW92}
Klaus Lux, R[ichard]~A. Parker, and R[obert]~A. Wilson.
\newblock {\em Modular Atlas of Finite Groups}.
\newblock To appear, 1993.

\bibitem[McK90]{Nau90}
B.D. McKay.
\newblock {\em {nauty} user's guide (version 1.5), Technical report
  TR-CS-90-02}.
\newblock Australian National University, Computer Science Department, ANU,
  1990.

\bibitem[McL77]{McL77}
D.~H. McLain.
\newblock An algorithm for determining defining relations of a subgroup.
\newblock {\em Glasgow Math. J.}, 18:51--56, 1977.

\bibitem[Mni92]{Mni92}
J{\accent127 u}rgen Mnich.
\newblock Untergruppenverb{\accent127 a}nde und aufl{\accent127 o}sbare
  {G}ruppen in {GAP}.
\newblock Diplom\-ar\-beit, Lehrstuhl D f{\accent127 u}r Mathematik, Rheinisch
  Westf{\accent127 a}lische Technische Hoch\-schule, Aachen, Germany, 1992.

\bibitem[Mon85]{Mon85}
Peter~L. Montgomery.
\newblock Modular multiplication without trial division.
\newblock {\em Math. Comput.}, 44:519--521, 1985.

\bibitem[MS85]{MS85}
John McKay and Leonard~H. Soicher.
\newblock Computing {G}alois groups over the rationals.
\newblock {\em J. Number Theory}, 20:273--281, 1985.

\bibitem[Mur58]{Mur58}
F[rancis]~D. Murnaghan.
\newblock The orthogonal and symplectic groups.
\newblock Communications Series A~13, Dublin Inst. Adv. Studies, 1958.

\bibitem[Neu67]{Neu67}
Joachim Neub{\accent127 u}ser.
\newblock {\em Die {U}ntergruppenverb{\accent127 a}nde der {Gruppen} der
  {Ordnungen} $\leq 100$ mit {Ausnahme} der {Ordnungen} 64 und 96}.
\newblock Habilitationsschrift, Universit{\accent127 a}t Kiel, Kiel, Germany,
  1967.

\bibitem[Neu82]{Neu82}
Joachim Neub{\accent127 u}ser.
\newblock An elementary introduction to coset table methods in computational
  group theory.
\newblock In Campbell and Robertson \cite{GrpsStAndrews81}, pages 1--45.

\bibitem[New77]{New77}
M[ichael]~F. Newman.
\newblock Determination of groups of prime-power order.
\newblock In R.~A. Bryce, J.~Cossey, and M[ichael]~F. Newman, editors, {\em
  Group theory, Proc. Miniconf., Austral. Nat. Univ., Canberra, 1975}, Lecture
  Notes in Math., vol. 573, pages 73--84. Springer, Berlin, 1977.

\bibitem[NO89]{NO89}
M[ichael]~F. Newman and E[amonn]~A. O{\accent19{}B}rien.
\newblock A {CAYLEY} library for the groups of order dividing 128.
\newblock In {\em Group Theory, Proceedings of the 1987 Singapore Conference,
  Singapore 1987}, pages 437--442. Walter de Gruyter, Berlin, New York, 1989.

\bibitem[NPP84]{NPP84}
J[oachim] Neub{\accent127 u}ser, H[erbert] Pahlings, and W[ilhelm] Plesken.
\newblock {CAS}; design and use of a system for the handling of characters of
  finite groups.
\newblock In Atkinson \cite{Durham82}, pages 195--247.

\bibitem[NPW81]{NPW81}
J[oachim] Neub{\accent127 u}ser, W[ilhelm] Plesken, and H[ans] Wondratschek.
\newblock An emendatory discursion on defining crystal systems.
\newblock {\em Match}, 10:77--96, 1981.

\bibitem[O{\accent19{}B}r90]{OBr90}
E[amonn]~A. O{\accent19{}B}rien.
\newblock The $p$-group generation algorithm.
\newblock {\em J. Symbolic Computation}, 9:677--698, 1990.

\bibitem[O{\accent19{}B}r91]{OBr91}
E[amonn]~A. O{\accent19{}B}rien.
\newblock The groups of order $256$.
\newblock {\em J. Algebra}, 142, 1991.

\bibitem[O{\accent19{}B}r93a]{OBr94}
E[amonn]~A. O{\accent19{}B}rien.
\newblock Computing automorphism groups of p-groups.
\newblock {\em CANT '92}, 1993.
\newblock submitted to Proceeding of CANT '92 (Sydney).

\bibitem[O{\accent19{}B}r93b]{OBr93}
E[amonn]~A. O{\accent19{}B}rien.
\newblock Isomorphism testing for p-groups.
\newblock {\em J. Symbolic Computation}, 17 (1), 1993.

\bibitem[Ost86]{Ost86}
Th[omas] Ostermann.
\newblock {C}haraktertafeln von {S}ylownormalisatoren sporadischer einfacher
  {G}ruppen.
\newblock Vorlesungen aus dem Fachbereich Mathematik~14, Universit{\accent127
  a}t Essen, Essen, Germany, 1986.

\bibitem[Pah93]{Pah93}
Herbert Pahlings.
\newblock On the {M\accent127 o}bius function of a finite group.
\newblock {\em Arch. Math.}, 1993.
\newblock To appear.

\bibitem[Ple90]{Ple90}
W[ilhelm] Plesken.
\newblock Additive decompositions of positive integral quadratic forms.
\newblock The paper is available at Lehrstuhl B f{\accent127 u}r Mathematik,
  Rheinisch Westf{\accent127 a}lische Technische Hoch\-schule Aachen, may be it
  will be published in the near future, 1990.

\bibitem[Poh87]{Poh87}
M[ichael] Pohst.
\newblock A modification of the lll reduction algorithm.
\newblock {\em J. Symbolic Computation}, 4:123--127, 1987.

\bibitem[Rin93]{Rin93}
Michael Ringe.
\newblock {\em The {C} {M}eat{A}xe, Release 1.5}.
\newblock Lehrstuhl D f{\accent127 u}r Mathematik, Rheinisch Westf{\accent127
  a}lische Technische Hoch\-schule, Aachen, Germany, 1993.

\bibitem[Rob88]{Rob88}
E[dmund]~F. Robertson.
\newblock {T}ietze transformations with weighted substring search.
\newblock {\em J. Symbolic Computation}, 6:59--64, 1988.

\bibitem[Sch90]{Sch90}
Gerhard J.~A. Schneider.
\newblock {D}ixon's character table algorithm revisited.
\newblock {\em J. Symbolic Computation}, 9:601--606, 1990.

\bibitem[Sho92]{Sho92}
Mark~W. Short.
\newblock {\em The Primitive Soluble Permutation Groups of Degree less than
  256}, volume 1519 of {\em Lecture Notes in Mathematics}.
\newblock Springer, Berlin and Heidelberg, 1992.

\bibitem[Sim70]{Sim70}
Charles~C. Sims.
\newblock Computational methods in the study of permutation groups.
\newblock In John Leech, editor, {\em Computational Problems in Abstract
  Algebra, Proc. Conf. Oxford, 1967}, pages 169--183. Pergamon Press, Oxford,
  1970.

\bibitem[Soi93]{Soi91}
L[eonard]~H. Soicher.
\newblock {GRAPE}: a system for computing with graphs and groups.
\newblock In L.~Finkelstein and B.~Kantor, editors, {\em Proceedings of the
  1991 DIMACS Workshop on Groups and Computation}, volume~11 of {\em DIMACS
  Series in Discrete Mathematics and Theoretical Computer Science}, pages
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\bibitem[Thi87]{Thi87}
Peter Thiemann.
\newblock {SOGOS} {III} - {C}haraktere und {E}ffizienzuntersuchung.
\newblock Diplom\-arbeit, Lehrstuhl D f{\accent127 u}r Mathematik, Rheinisch
  Westf{\accent127 a}lische Technische Hoch\-schule, Aachen, Germany, 1987.

\bibitem[vdW76]{vdW76}
Robert~W. van~der Waall.
\newblock On symplectic primitive modules and monomial groups.
\newblock {\em Indagationes Math.}, 38:362--375, 1976.

\bibitem[VL84]{Vau84}
M[ichael]~R. Vaughan-Lee.
\newblock An aspect of the nilpotent quotient algorithm.
\newblock In Atkinson \cite{Durham82}, pages 75--84.

\bibitem[VL90a]{Vau90b}
M[ichael]~R. Vaughan-Lee.
\newblock Collection from the left.
\newblock {\em J. Symbolic Computation}, 9:725--733, 1990.

\bibitem[VL90b]{Vau90a}
M[ichael]~R. Vaughan-Lee.
\newblock {\em The restricted {Burnside} problem}, volume~5 of {\em London
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\newblock Clarendon, Oxford, 1990.

\bibitem[Wur93]{Wur93}
Martin Wursthorn.
\newblock {\em {\sc SISYPHOS} Computing in modular group algebras, Version
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\newblock Math. Inst. B, 3. Lehrstuhl, Universit{\accent127 a}t Stuttgart,
  1993.

\bibitem[Zum89]{Zum89}
Matthias Zumbroich.
\newblock {Grundlagen} einer {Arithmetik} in {Kreisteilungsk{\accent127
  o}rpern} und ihre {Implementation} in {CAS}.
\newblock Dimplomarbeit, Lehrstuhl D f{\accent127 u}r Mathematik, Rheinisch
  Westf{\accent127 a}lische Technische Hoch\-schule, Aachen, Germany, 1989.

\end{thebibliography}