+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ + + + Copyright (C) 2013 Andreas Distler + + + + This file is part of `SpecialExt'. + + + + `SpecialExt' is free software: you can redistribute it and/or modify + + it under the terms of the GNU General Public License as published by + + the Free Software Foundation, either version 2 of the license, or + + (at your option) any later version. + + + + `SpecialExt' is distributed in the hope that it will be useful, + + but WITHOUT ANY WARRANTY; without even the implied warranty of + + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + + GNU General Public License for more details. + + + + A copy of the GNU General Public License is available in the file + + `COPYING'; or for later versions see . + + + + You can find contact information at the end of this file. + + + +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ This is the README file for the GAP package `SpecialExt'. SpecialExt contains functions to construct group extensions of an elementary abelian group A with a group G which are of special type. The group A will either be the last non-trivial term in the lower central series or in the derived series of the extension. -------------- Requirements -------------- This software is written for GAP 4. It requires an existing installation of GAP (see www.gap-system.org) in version 4.5 or higher. One file in the GAP library needs to be altered for the package to work in full, see `Installation' below. -------------- Installation -------------- Part A: The first part of the installation follows standard GAP rules as outlined in the following steps; see Section 74.1 in the reference manual of GAP for further details: 1) Download the archive `SpecialExt-0.2.tar.gz' from http://www.icm.tu-bs.de/ag_algebra/software/SpecialExt 2) Move the archive inside a `pkg' directory. This can be either the main 'pkg' directory in your GAP installation or your personal 'pkg' directory. 3) Complete the installation by unpacking the archive, e.g. under Linux type tar -xzf SpecialExt-0.2.tar.gz at the prompt for the gzipped tar-archive. A subdirectory `SpecialExt-0.2' will be created inside the `pkg' directory. Part B: The file `grppcext.gi' in the subdirectory lib of the GAP installation needs to be altered for the package to work in full. Applying the patch file `patch-MatrixOperationOfCPGroup.txt' from the package to `grppcext.gi' will perform the necessary alterations. Under GNU/Linux you can use the command patch lib/grppcext.gi pkg/SpecialExt/patch-MatrixOperationOfCPGroup.txt from the GAP main directory provided you installed SpecialExt in the main `pkg' directory of your GAP installation. If you prefer editing `grppcext.gi' by hand add the three lines if not tails in Source(cc.cohom) then return fail; fi; near the end of the function MatrixOperationOfCPGroup just before tails := Image( cc.cohom, tails ); ConvertToVectorRepNC(tails,field); Add( mats[l], tails ); --------------- Functionality --------------- The main functionality are the computation of lower central series extensions and derived series extensions up to isomorphism using the commands LowerCentralExtensionRepresentatives respectively DerivedSeriesExtensionsSQ The three examples of groups of derived length 10 and composition length 24 from the article `Group extensions with special properties' can be accessed giving 1, 2 or 3 as input to the function ExampleDerivedLength10Group ------------ Background ------------ Theoretical background for the algorithms in the package can be found in the article `Group extensions with special properties' by Andreas Distler and Bettina Eick. --------- Contact --------- Andreas Distler TU Braunschweig AG Algebra und Diskrete Mathematik Rebenring 31 (A14) 38106 Braunschweig Germany