# The IRREDSOL package

A Library of irreducible solvable linear groups over finite fields

Author:
  Burkhard Höfling, e-mail: b.hoefling@tu-bs.de
Language:
  GAP 4.3
Operating System:
  any
Current version:
  1.0.2
Home page:
  http://www.tu-bs.de/~bhoeflin/irredsol/index.htm

## Description

Let n be a positive integer and q a prime power satisfying q^n < 65536. The package IRREDSOL constitutes a library of irreducible solvable subgroups of GL(n, q), such that each irreducible solvable subgroup of GL(n, q) is conjugate to precisely one group in the library.

This data base is intended to replace and extend the data base of irreducible matrix groups over prime fields created by Mark Short \cite{Sho which is also part of GAP. There are functions available to translate from Mark Short's numbering of groups to the numbering used in IRREDSOL and back.

It is possible to construct groups in this list one at a time, by supplying four integer parameters identifying the group in question. In addition, there are functions which facilitate searching the library for groups with given properties.

Given an irreducible solvable matrix group G, it is possible to find the group in the library to which G is conjugate.

Moreover,, the IRREDSOL package provides additional functionality for matrix groups, such as the computation of imprimitivity systems.

Finally, the library of irreducible solvable matrix groups over prime fields translates into a library of isomorphism types of primitive solvable groups. There are functions avalable which faciliate this translation.

## IRREDSOL manual

- HTML: Table of Contents, Index
- TEX dvi version
- Adobe Acrobat PDF version