Let <M>KG</M> be a group algebra of a finite <M>p</M>-group <M>G</M>
over the field <M>K</M> of characteristic <M>p</M>, and let <M>V(KG)</M>
be the normalized unit group of <M>KG</M>.
The pc-presentation of the group <M>V(KG)</M>
can be computed using the &GAP; package &LAGUNA;
(<URL>https://gap-packages.github.io/laguna/</URL>),
but for groups of orders 64 and more such computation will already
take a lot of time.
<P/>
The &UnitLib; package is an extension of the &LAGUNA; package that is
focused on this problem. It contains the library of normalized unit groups
of modular group algebras of finite <M>p</M>-groups over the field
of <M>p</M> elements. This allows the user to retrieve the pre-computed
group from the library instead of the time-consuming computation. The group
created with &UnitLib; will have the same properties and attributes as
the one computed with &LAGUNA;.
<P/>
The version &UnitLib; 3.0.0 released in May 2009 also contained a parallel
implementation of the computation of the normalized unit group of a modular
group algebra of a finite <M>p</M>-group over the field of <M>p</M> elements,
which works for groups from the &GAP; small groups library. It is developed
on the base of the sequential version of this algorithm (which works for
any <M>p</M>-group with no limitations) from the &LAGUNA; package.
Parallelisation is implemented using the &SCSCP; package that is capable of
connecting several local or remote &GAP; instances using the &SCSCP; protocol.
<P/>
In April 2012, &UnitLib; 3.1.0 was updated to comply with &GAP; 4.5.
<P/>
The current version of &UnitLib; provides the library of
normalized unit groups <M>V(KG)</M> for all <M>p</M>-groups
of order up to 243.
<P/>
If you need to work with groups of bigger orders, please write to
the maintainers, because they may be already computed or we
can compute them for you.
<P/>
Since the &UnitLib; package is an extension of the &LAGUNA; package
<Cite Key="Laguna"/>, we refer to the
<Ref Label="LAGUNA package" BookName="LAGUNA"/> manual for the theoretical
backround. In particular, Chapter 3
(The basic theory behind &LAGUNA;) of that manual contains definitions
of the modular group algebra and its normalized unit group, the
power-commutator presentation of the group, and also more details about the
algorithm for the computation of the pc-presentation of the normalized unit
group of a modular group algebra of a finite <M>p</M>-group.
</Section>
<Section Label="Install">
<Heading>Installation and system requirements</Heading>
&UnitLib; &VERSION; requires at least &GAP; 4.10.
The libraries of normalized unit groups of groups of orders less than 243
are included in the distribution. The data for order 243 is available as
an optional download.
<P/>
Because the &UnitLib; is an extension of the &LAGUNA; package, you must
have the &LAGUNA; package installed. You can obtain it from the &GAP;
homepage or from its homepage
<URL>https://gap-packages.github.io/laguna/</URL>.
<P/>
To use the &UnitLib; online help it is necessary to install the &GAP;4 package
&GAPDoc; by Frank Lübeck and Max Neunhöffer, which is available from the
&GAP; homepage or from
<URL>http://www.math.rwth-aachen.de/˜Frank.Luebeck/GAPDoc/</URL>.
<P/>
&UnitLib; is distributed in standard formats
(<File>tar.gz</File>, <File>tar.bz2</File>, <File>.zip</File>,
<File>-win.zip</File>) and can be obtained from the &GAP; homepage or from
<URL>https://gap-packages.github.io/unitlib/</URL>.
To install &UnitLib;, unpack its archive into the <File>pkg</File>
subdirectory of your &GAP; installation. When you don't have access
to the directory of your main &GAP; installation, you can also install
the package <E>outside the &GAP; main directory</E>
by unpacking it inside a directory <File>MYGAPDIR/pkg</File>.
Then to be able to load &UnitLib; you need to call &GAP; with the
<C>-l ";MYGAPDIR"</C> option.
<P/>
</Section>
</Chapter>
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