Given a finitely generated group $G$ and a normal subgroup of finite index $K$, how can I use GAP to find a list of coset representatives, and also show that two coset representatives are equal?
2026-03-25 06:24:59.1774419899
Using GAP to find coset representatives
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You could use
FactorCosetAction(G,K)to obtain the permutation action of G on the cosets of K and use images of elements (i.e. where do they map 1) under this homomorphism to identify cosets. AlsoAsList(RightTransversal(g,k));will give you coset representatives (for any subgroup, normal not required). PErformance of course will depend on the index of $K$.