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#     Australian National University p-Quotient Program 
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#     Version 1.2
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#     April 1994
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This implementation was developed in C by 

Eamonn O'Brien 
School of Mathematical Sciences
Australian National University
Canberra, ACT 0200

e-mail obrien@maths.anu.edu.au
Telephone +61-(0)6-249 2963 (office)
FAX +61-(0)6-249 5549 

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The program provides access to implementations of the following algorithms:

1. A p-quotient algorithm to compute a power-commutator presentation
for a p-group.  The algorithm implemented here is based on that 
described in Havas and Newman (1980) and papers referred to there.
Another description of the algorithm appears in Vaughan-Lee (1990).
A FORTRAN implementation of this algorithm was programmed by 
Alford & Havas. The basic data structures of that implementation 
are retained.

The current implementation incorporates the following features:

a. collection from the left (see Vaughan-Lee, 1990); 
   Vaughan-Lee's implementation of this collection 
   algorithm is used in the program;

b. an improved consistency algorithm (see Vaughan-Lee, 1982);

c. new exponent law enforcement and power routines; 

d. closing of relations under the action of automorphisms;

e. some formula evaluation.

For details of these latter improvements, see 
Newman and O'Brien (in preparation). 

2. A p-group generation algorithm to generate descriptions of p-groups. 
The algorithm implemented here is based on the algorithms described in 
Newman (1977) and O'Brien (1990). A FORTRAN implementation of this 
algorithm was earlier developed by Newman & O'Brien.  

3. A standard presentation algorithm used to compute a canonical 
power-commutator presentation of a p-group. The algorithm 
implemented here is described in O'Brien (1993).

4. An algorithm which can be used to compute the automorphism group of 
a p-group. The algorithm implemented here is described in O'Brien (1994).

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George Havas and M.F. Newman (1980), "Application of computers
to questions like those of Burnside", Burnside Groups (Bielefeld, 1977), 
Lecture Notes in Math. 806, pp. 211-230. Springer-Verlag.

M.F. Newman (1977), "Determination of groups of prime-power order", 
Group Theory (Canberra, 1975). Lecture Notes in Math. 573, pp. 73-84. 
Springer-Verlag.

M.F. Newman and E.A. O'Brien (in preparation), "Application of computers to 
questions like those of Burnside II".

E.A. O'Brien (1990), "The p-group generation algorithm",
J. Symbolic Comput. 9, 677-698.

E.A. O'Brien (1993), ``Isomorphism testing for p-groups", 
J. Symbolic Comput. 17 (1).

E.A. O'Brien (1994), ``Computing automorphism groups of p-groups", 
to appear in Proceeding of CANT '92 (Sydney).

M.R. Vaughan-Lee (1982), "An Aspect of the Nilpotent Quotient Algorithm", 
Computational Group Theory (Durham, 1982), pp. 76-83. Academic Press.

Michael Vaughan-Lee (1990), The Restricted Burnside Problem,
London Mathematical Society monographs (New Ser.) #5.
Clarendon Press, New York, Oxford.

M.R. Vaughan-Lee (1990), "Collection from the left", 
J. Symbolic Comput. 9, 725-733.

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