1<Chapter Label="Intro"> 2<Heading>Introduction</Heading> 3 4<Section Label="Aims"> 5<Heading>General aims</Heading> 6 7Let <M>KG</M> be a group algebra of a finite <M>p</M>-group <M>G</M> 8over the field <M>K</M> of characteristic <M>p</M>, and let <M>V(KG)</M> 9be the normalized unit group of <M>KG</M>. 10 11The pc-presentation of the group <M>V(KG)</M> 12can be computed using the &GAP; package &LAGUNA; 13(<URL>https://gap-packages.github.io/laguna/</URL>), 14but for groups of orders 64 and more such computation will already 15take a lot of time. 16<P/> 17 18The &UnitLib; package is an extension of the &LAGUNA; package that is 19focused on this problem. It contains the library of normalized unit groups 20of modular group algebras of finite <M>p</M>-groups over the field 21of <M>p</M> elements. This allows the user to retrieve the pre-computed 22group from the library instead of the time-consuming computation. The group 23created with &UnitLib; will have the same properties and attributes as 24the one computed with &LAGUNA;. 25<P/> 26The version &UnitLib; 3.0.0 released in May 2009 also contained a parallel 27implementation of the computation of the normalized unit group of a modular 28group algebra of a finite <M>p</M>-group over the field of <M>p</M> elements, 29which works for groups from the &GAP; small groups library. It is developed 30on the base of the sequential version of this algorithm (which works for 31any <M>p</M>-group with no limitations) from the &LAGUNA; package. 32Parallelisation is implemented using the &SCSCP; package that is capable of 33connecting several local or remote &GAP; instances using the &SCSCP; protocol. 34<P/> 35In April 2012, &UnitLib; 3.1.0 was updated to comply with &GAP; 4.5. 36<P/> 37The current version of &UnitLib; provides the library of 38normalized unit groups <M>V(KG)</M> for all <M>p</M>-groups 39of order less than 243. 40<P/> 41If you need to work with groups of bigger orders, please write to 42the maintainers, because they may be already computed or we 43can compute them for you. 44<P/> 45 46</Section> 47 48<Section Label="TheoryUnitlib"> 49<Heading>Theoretical background</Heading> 50 51Since the &UnitLib; package is an extension of the &LAGUNA; package 52<Cite Key="Laguna"/>, we refer to the 53<Ref Label="LAGUNA package" BookName="LAGUNA"/> manual for the theoretical 54backround. In particular, Chapter 3 55(The basic theory behind &LAGUNA;) of that manual contains definitions 56of the modular group algebra and its normalized unit group, the 57power-commutator presentation of the group, and also more details about the 58algorithm for the computation of the pc-presentation of the normalized unit 59group of a modular group algebra of a finite <M>p</M>-group. 60 61</Section> 62 63 64<Section Label="Install"> 65<Heading>Installation and system requirements</Heading> 66 67&UnitLib; &VERSION; is designed for &GAP; 4.5 and no compatibility with 68previous releases of &GAP; 4 is guaranteed. 69<P/> 70 71Libraries of normalized unit groups of groups of orders less than 243, 72except for the order 128, will be available in any operating system. 73<P/> 74 75The library for groups of order 76128 was compressed using the <File>gzip</File> program and, therefore, 77will be available only in UNIX-type systems (including UNIX-installation 78in Mac OS X and Cygwin installation in Windows). If you need to work with 79groups of order 128 in Windows, please write to the maintainer to request 80a version of &UnitLib; with locally stored non-compressed data. 81<P/> 82 83<!-- 84To work with the library for groups of order 243 you will also need the 85<Package>IO</Package> package by Max Neunhöffer 86(<URL>https://gap-packages.github.io/io/</URL>) 87to retrieve the data from the &UnitLib; homepage. 88<P/> 89--> 90 91Because the &UnitLib; is an extension of the &LAGUNA; package, you must 92have the &LAGUNA; package installed. You can obtain it from the &GAP; 93homepage or from its homepage 94<URL>https://gap-packages.github.io/laguna/</URL>. 95<P/> 96 97To use the &UnitLib; online help it is necessary to install the &GAP;4 package 98&GAPDoc; by Frank Lübeck and Max Neunhöffer, which is available from the 99&GAP; homepage or from 100<URL>http://www.math.rwth-aachen.de/˜Frank.Luebeck/GAPDoc/</URL>. 101<P/> 102 103&UnitLib; is distributed in standard formats 104(<File>tar.gz</File>, <File>tar.bz2</File>, <File>.zip</File>, 105<File>-win.zip</File>) and can be obtained from the &GAP; homepage or from 106<URL>https://gap-packages.github.io/unitlib/</URL>. 107To install &UnitLib;, unpack its archive into the <File>pkg</File> 108subdirectory of your &GAP;4.5 installation. When you don't have access 109to the directory of your main &GAP; installation, you can also install 110the package <E>outside the &GAP; main directory</E> 111by unpacking it inside a directory <File>MYGAPDIR/pkg</File>. 112Then to be able to load &UnitLib; you need to call &GAP; with the 113<C>-l ";MYGAPDIR"</C> option. 114<P/> 115 116</Section> 117 118</Chapter>