We are interested in the following problem:
Decompose a finite *abelian permutation group* into
a direct product of cyclic p-groups.
It is well-known that the orders of the factors are
uniquely determined. They can be computed fast by
AbelianInvariants(G). In addition if G is given as
the quotient of a free Z-module with a relator module
the Smith-normal form computation will solve the
problem. Thus the question for us is:
Is there a way of avoiding the computation of an
Fp-representation for the permutation group in order
to compute the generators of cyclic p-groups?
Alternatively: Is there a fast way to compute a
word presentation for an abelian *permutation* group?