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How to construct direct product of cyclic groups

asked 2022-09-01 11:15:56 +0200

abhijitg gravatar image

updated 2022-09-01 11:40:56 +0200

FrédéricC gravatar image

If I use

D = direct_product_permgroups([G1,G2])


G1 = CyclicPermutationGroup(3)
G2 = CyclicPermutationGroup(4)

then I get D presented as a subgroup of SymmetricGroup(7). Is there a way to obtain the product of G1 and G2 as a subgroup of SymmetricGroup(12)?

More generally, is there a way to obtain direct product of CyclicPermutationGroup(n1) and CyclicPermutationGroup(n2) as a subgroup of SymmetricGroup(n1 n2) rather than SymmetricGroup(n1+n2)?

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answered 2022-09-01 12:04:41 +0200

abhijitg gravatar image

updated 2022-09-01 12:04:57 +0200

By trial and error I found the answer:

K = D.as_finitely_presented_group()

H = K.as_permutation_group()

This gives the desired presentation of D.

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Asked: 2022-09-01 11:15:56 +0200

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Last updated: Sep 01 '22