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/&tilde;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>