Dear Jacob, dear Forum,
what you can do is to represent your group as a permutation group
acting on the integers. Then such computations are easy:
gap> LoadPackage("rcwa");
gap> AllTransitiveGroups(DegreeAction,12,Size,60);
[ A_5(12) ]
gap> A5 := last[1]; # your A5 embedded in S12
A_5(12)
gap> F1 := CyclicGroup(IsRcwaGroupOverZ,infinity);
<tame rcwa group over Z with 1 generator, of order infinity>
gap> G := WreathProduct(F1,A5);
<tame rcwa group over Z with 3 generators, of order infinity>
gap> P := RespectedPartition(G);
[ 0(12), 1(12), 2(12), 3(12), 4(12), 5(12), 6(12), 7(12), 8(12), 9(12),
10(12), 11(12) ]
gap> t0 := G.1*G.2;; # choose any subgroup generators
gap> t1 := G.2*G.3^2;; #
gap> H := Group(t0,t1);
<rcwa group over Z with 2 generators>
gap> Permutation(t0*t1,P); # compute image under projection
(1,11)(2,3)(4,6)(5,7)(8,9)(10,12)
If you need to form homomorphism objects performing in this way,
then you would need to add suitable methods to the RCWA package
(that being a routine task -- it just hasn't been done so far).
Does this help you?
Stefan
P.S.: Just in case -- the repository for RCWA is here:
https://github.com/gap-packages/rcwa
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https://stefan-kohl.github.io/
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Am 09.02.2018 um 19:44 schrieb Jacob Bond:
Hi,
I have constructed F1 wr A5, where F1 is the free group on 1 generator and A5
is embedded in S12, and have the projection map of the wreath product.
However, I would like to restrict the projection to a subgroup of the wreath
product given by two generators t0, t1. I've tried constructing the
restriction in a few different ways: RestrictedMapping,
GroupHomomorphismByImages, and GroupHomomorphismByFunction. None of these
would return, and while GroupHomomorphismByImagesNC returned the homomorphism,
it was unable to compute the image even of t0*t1. Is there a better way to
construct the restriction of the projection map? Or am I probably out of luck?
Thank you,
Jacob
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