23.6 IsIdenticalPresentationFpGroup

IsIdenticalPresentationFpGroup( G, H )

IsIdenticalPresentationFpGroup returns true if the presentations of the parent groups G and H are identical and false otherwise.

Two presentations are considered identical if the have the same number of generators, i.e., G is generated by g1 ... gn and H by h1 ... hn, and if the set of relators of G stored in G.relators is equal to the set of relators of H stored in H.relators after replacing hi by gi in these words.

    gap> F2 := FreeGroup(2);
    Group( f.1, f.2 )
    gap> g := F2 / [ F2.1^2 / F2.2 ];
    Group( f.1, f.2 )
    gap> h := F2 / [ F2.1^2 / F2.2 ];
    Group( f.1, f.2 )
    gap> g = h;
    false
    gap> IsIdenticalPresentationFpGroup( g, h );
    true 

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