Let H and G_1, \ldots, G_n be groups. For each i \in \{1,\ldots,n\}, let g_i,g_i' \in G_i and let \varphi_i,\psi_i\colon H \to G_i be group homomorphisms. The multiple twisted conjugacy problem is the problem of finding some h \in H such that g_i = \psi_i(h)g_i'\varphi_i(h)^{-1} for all i \in \{1,\ldots,n\}.
‣ IsTwistedConjugateMultiple( hom1List[, hom2List], g1List[, g2List] ) | ( function ) |
Verifies whether the multiple twisted conjugacy problem for the given homomorphisms and elements has a solution.
‣ RepresentativeTwistedConjugationMultiple( hom1List[, hom2List], g1List[, g2List] ) | ( function ) |
Computes a solution to the multiple twisted conjugacy problem for the given homomorphisms and elements, or returns fail if no solution exists.
gap> H := SymmetricGroup( 5 );; gap> G := AlternatingGroup( 6 );; gap> tau := GroupHomomorphismByImages( H, G, [ (1,2)(3,5,4), (2,3)(4,5) ], > [ (1,3)(4,6), () ] );; gap> phi := GroupHomomorphismByImages( H, G, [ (1,2)(3,5,4), (2,3)(4,5) ], > [ (1,2)(3,6), () ] );; gap> psi := GroupHomomorphismByImages( H, G, [ (1,2)(3,5,4), (2,3)(4,5) ], > [ (1,4)(3,6), () ] );; gap> khi := GroupHomomorphismByImages( H, G, [ (1,2)(3,5,4), (2,3)(4,5) ], > [ (1,2)(3,4), () ] );; gap> IsTwistedConjugateMultiple( [ tau, phi ], [ psi, khi ], > [ (1,5)(4,6), (1,4)(3,5) ], [ (1,4,5,3,6), (2,4,5,6,3) ] ); true gap> RepresentativeTwistedConjugationMultiple( [ tau, phi ], [ psi, khi ], > [ (1,5)(4,6), (1,4)(3,5) ], [ (1,4,5,3,6), (2,4,5,6,3) ] ); (1,2)
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