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# How to create a morphism between a permutation groups and a matrix groups by explicitley giving the map?

I looking to define a homomorphism between a permutation group to another permutation group by defining the map explicitly. Same between matrix groups? Can some body help? For example The following codes gives an error

sage: G = SymmetricGroup(5)
sage: r = G('(1,3,5,2,4)')
sage: s = G('(2,5),(3,4)')
sage: H = G.subgroup([r,s])
sage: D = DihedralGroup(5)
sage: (a,b)= D.gens()
phi = PermutationGroupMorphism(H,D, [a,b])
phi(x)

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## 1 Answer

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First, phi(x) does not makes much sense since x benongs to the symbolic ring, and has nothing to do with your group H.

However, i agree that the following seems and issue:

sage: phi(r)
RuntimeError: Gap produced error output
Error, usage: Image(<map>), Image(<map>,<elm>), Image(<map>,<coll>)

executing __SAGE_LAST__:="__SAGE_LAST__";;Image(\$sage11,\$sage9);;


And even:

sage: phi(H(r))
RuntimeError: Gap produced error output
Error, usage: Image(<map>), Image(<map>,<elm>), Image(<map>,<coll>)

executing __SAGE_LAST__:="__SAGE_LAST__";;Image(\$sage21,\$sage20);;


Thanks for reporting, someone should have a deeper look and see what does gap return to understand.

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## Comments

Thanks, I shall wait for someone to resolve this issue!

( 2018-10-02 11:13:48 +0200 )edit

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Asked: 2018-10-02 02:20:02 +0200

Seen: 173 times

Last updated: Oct 02 '18