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<Abstract>

&RCWA; is a package for &GAP;&nbsp;4. It provides implementations of
algorithms and methods for computing in certain infinite permutation 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>\mathbb{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>(\mathbb{Z},+)</M>.
  </Item>

</List>

With substancial help of this package, the author has found a countable
simple group which has an uncountable series of simple subgroups.
This simple group is generated by involutions which interchange disjoint
residue classes of the integers. All the above groups embed into it. <P/>

</Abstract>

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