Sophie

Sophie

distrib > Mandriva > 2010.0 > i586 > media > contrib-release > by-pkgid > 5e1854624d3bc613bdd0dd13d1ef9ac7 > files > 3313

gap-system-4.4.12-5mdv2010.0.i586.rpm

  
  1. Introduction
  
  
  1.1 General aims
  
  Let  KG  be  a  group  algebra  of  a  finite  p-group G over the field K of
  characteristic  p,  and  let  V(KG)  be the normalized unit group of KG. The
  pc-presentation  of  the  group  V(KG) can be computed using the GAP package
  LAGUNA (http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm), but for groups of
  orders 64 and more such computation will already take a lot of time.
  
  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 p-groups over the field of p elements. This allows
  the  user to retrieve the pre-computed group from the library instead of the
  long-time  computation.  The  group  created with UnitLib will have the same
  properties and attributes as the one computed with LAGUNA.
  
  The  current  version  of  UnitLib  provides  the library of normalized unit
  groups  V(KG) for all p-groups of order not greater than 243. If you need to
  work  with  groups of bigger orders, please write to the authors, because we
  may already have them computed or can compute them for you.
  
  
  1.2 Theoretical background
  
  Since  the  UnitLib  package is an extension of the LAGUNA package [BK+], we
  refer to the LAGUNA: LAGUNA package 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 p-group.
  
  
  1.3 Installation and system requirements
  
  UnitLib  is  designed for GAP4.4 and no compatibility with previous releases
  of GAP4 is guaranteed.
  
  Libraries  of  normalized  unit  groups  of  groups of orders less than 243,
  except for the order 128, will be available in any operating system.
  
  The  library  for  groups of order 128 was compressed using the gzip program
  and,  therefore,  will  be  available  only  in UNIX-type systems (including
  UNIX-installation in Mac OS X and Cygwin installation in Windows).
  
  To work with the library for groups of order 243 you will also need the Curl
  program   (http://curl.haxx.se)  to  retrieve  the  data  from  the  UnitLib
  homepage,          and          the         GAP         package         Qaos
  (http://www.gap-system.org/Packages/qaos.html)   which   provides   the  GAP
  function Curl to work with cURL.
  
  If  you  need to work with groups of order 128 or 243 in Windows environment
  or  you  can  not  use Curl, please write to the authors. We will be able to
  give you a version of UnitLib with locally stored non-compressed data.
  
  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 http://www.cs.st-andrews.ac.uk/~alexk/laguna.htm.
  
  To  use  the UnitLib online help it is necessary to install the GAP4 package
  GAPDoc  by  Frank L\"ubeck and Max Neunh\"offer, which is available from the
  GAP homepage or from http://www.math.rwth-aachen.de/~Frank.Luebeck/GAPDoc/.
  
  UnitLib  is distributed in standard formats (zoo, tar.gz, tar.bz2, -win.zip)
  and    can    be    obtained    from    the    GAP    homepage    or    from
  http://www.cs.st-andrews.ac.uk/~alexk/unitlib.htm.  To  unpack  the  archive
  unitlib-2.1.zoo  you  need the program unzoo, which can be obtained from the
  GAP  homepage  http://www.gap-system.org/  (see  section `Distribution'). To
  install  UnitLib, copy this archive into the pkg subdirectory of your GAP4.4
  installation.  Then  the subdirectory unitlib containing the package will be
  created in the pkg directory after the command
  
  unzoo -x unitlib-2.1.zoo