23.5 OperationCosetsFpGroup

OperationCosetsFpGroup( G, H )

OperationCosetsFpGroup returns the permutation representation of the finitely presented group G on the cosets of the subgroup H as a permutation group. Note that this permutation representation is faithful if and only if H has a trivial core in G.

    gap> F2 := FreeGroup( "a", "b" );
    Group( a, b )
    gap> A5 := F2 / [ F2.1^2, F2.2^3, (F2.1*F2.2)^5 ];
    Group( a, b )
    gap> OperationCosetsFpGroup( A5,
    >            Subgroup( A5, [ A5.1, A5.2*A5.1*A5.2*A5.1*A5.2^-1 ] ) );
    Group( (2,3)(4,5), (1,2,4) )
    gap> Size( last );
    60 

OperationCosetsFpGroup simply calls CosetTableFpGroup, applies PermList to each row of the table, and returns the group generated by those permutations (see CosetTableFpGroup, PermList).

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