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Stephan Rosebrock asked for a function that tests if there is a

homomorphism of a finitely presented group into a given symmetric (or

alternating) group. Jacob Hirbawi explained, how to use the table of

marks of the finitely presented group for this task. This will of

course only work if the finitely presented group is also finite (and

not too big) so that GAP can calculate its table of marks, but then it

is a nice method.

However there is also a method to find permutation representations of

a finitely presented group of a given (not too big) degree (i.e.

homomorhisms into a given symmetric group of not too big degree),

which does not at all assume that the finitely presented group is

finite, namely the so-called Low Index Method which is implemented in

GAP by the function LowIndexSubgroupsFpGroup, described in section

22.6, page 419 of the manual of GAP 3. The practical limitation of the

degree for which the method will work depends strongly on the number

of generators of the finitely presented group but it has proved a

rather useful tool for the investigation of several finitely presented

groups that appeared in the literature. If wanted I can provide some

references.

Joachim Neubueser

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