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Hi!

First, I am a relatively new user of GAP, as well as a novice on

group theory. My question is...

I am trying to explicitly find all sub-direct products of the direct

product group SxGxS, where S and G are both 2-groups, which have the

property that the subgroup of elements of the form {(e,g,s)} (e is

identity of S, g is in G and s is in S) have a particular order (such as 4).

The size of S is typically 8,16 or 32 while G is 32, 64 or 128.

My questions are...

1) In general, does anyone have any guidelines as to the most efficient

presentations of these groups for calculation in GAP?

2) In specific, does anyone have ideas for a good course of action for

this problem.

I have so far been trying to use the Ag presentations from the 2-groups

library for S and G then forming the DirectProduct. GAP seems to compute

with this presentation fairly fast, but clearly an attempt to, say, use

Lattice seems futile (the direct products are 2k-128K in size!).

Anyway, any input would be greatly appreciated, particularly as to whether

the representation from the 2-group library or a permutation rep would

be more efficient.

thanks...

-eric (ejr@ee.cornell.edu)

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