<!-- #################################################################### -->
<!-- ##                                                                ## -->
<!-- ##  abstract.xml         RCWA documentation          Stefan Kohl  ## -->
<!-- ##                                                                ## -->
<!-- ##  $Id: abstract.xml,v 1.40 2006/09/29 10:38:16 stefan Exp $     ## -->
<!-- ##                                                                ## -->
<!-- #################################################################### -->

<Abstract>

&RCWA; is a package for &GAP; 4, which provides methods for computing with
<E>R</E>esidue <E>C</E>lass-<E>W</E>ise <E>A</E>ffine groups. In principle,
this package can deal at least with the following types of groups and their
subgroups:

<List>

  <Item>
    Finite groups, and certain divisible torsion groups which they
    embed into.
  </Item>

  <Item>
    Free groups of finite rank.
  </Item>

  <Item>
    Free products of finitely many finite groups, thus in particular
    the modular group PSL(2,<M>\Z</M>).
  </Item>

  <Item>
    Direct products of the above groups.
  </Item>

  <Item>
    Wreath products of the above groups with finite groups and
    with&nbsp;<M>(\Z,+)</M>.
  </Item>

</List>

With substancial help of this package, the author has found a countable
simple group which is generated by involutions interchanging residue classes
of the integers and into which all the above groups embed.
This simple group has an uncountable series of simple subgroups, which
is parametrized by the sets of odd primes. <P/>

</Abstract>

<!-- #################################################################### -->
