############################################################################
#
#              Matrix Group and G-Module library 
#
#                  Version 1.0, April 1994 
#
############################################################################
#
# The Library 
# 
############################################################################

This library provides functions which may be used to construct
and investigate the structure of matrix groups defined over finite
fields. These functions permit the user to construct certain types 
of matrix groups and G-modules; to test whether a G-module is 
irreducible or absolutely irreducible; to decide whether a group 
has certain decomposition with respect to a normal subgroup; 
and to select random elements with certain properties.

The code was developed as part of the on-going project to "recognise" 
the Aschbacher categories of matrix groups defined over finite fields. 

############################################################################
#
#Contents 
# 
############################################################################

The matrix directory contains the following subdirectories:

code -- the GAP files for the various functions.
doc --  gmodule.tex, gmodule.dvi, gmodule.ps, which describe the various
        functions and provide examples. This documentation is in 
        GAP format and can be read on-line in GAP.
    
papers -- The .dvi and .ps versions of the papers mentioned below.  

#############################################################################
#
#References
#
#############################################################################

The interested reader is referred to the following papers
for details of the algorithms used.

Derek F. Holt and Sarah Rees,  ``Testing modules for irreducibility'',
J. Austral. Math. Soc. Ser. A, 57, 1994.

Derek F. Holt, Charles R. Leedham-Green, E.A. O'Brien and Sarah Rees,
``Computing matrix group decompositions with respect to a normal
subgroup'',  submitted to London Math. Soc., 1994.

Derek F. Holt, Charles R. Leedham-Green, E.A. O'Brien and Sarah Rees,
``Primitivity testing for matrix groups'', submitted to London
Math. Soc., 1994.

############################################################################
#
# The Developers   
# 
############################################################################

Derek Holt, Mathematics Institute, Warwick  
dfh@maths.warwick.ac.uk

Charles Leedham-Green, School of Mathematical Studies, QMW 
C.R.Leedham-Green@qmw.ac.uk

Eamonn O'Brien, School of Mathematical Sciences, ANU 
Eamonn.OBrien@maths.anu.edu.au

Sarah Rees, Department of Mathematics and Statistics, Newcastle
Sarah.Rees@newcastle.ac.uk

