25.45 InitSQ

InitSQ( G )

Let G be a finitely presented group. InitSQ computes an SQ record for the commutator factor group of G. This record can be used to investigate finite solvable quotients of G .

Note that the commutator factor group of G must be finite otherwise an error message is printed.

See also ModulesSQ and NextModuleSQ.

    gap> f := FreeGroup( "a", "b", "c", "d" );;
    gap> f4 := f / [ f.1^2, f.2^2, f.3^2, f.4^2, f.1*f.2*f.1*f.2*f.1*f.2,
    >       f.2*f.3*f.2*f.3*f.2*f.3*f.2*f.3, f.3*f.4*f.3*f.4*f.3*f.4,
    >       f.1^-1*f.3^-1*f.1*f.3, f.1^-1*f.4^-1*f.1*f.4,
    >       f.2^-1*f.4^-1*f.2*f.4 ];;
    gap> s := InitSQ(f4);
    << solvable quotient of size 2^2 >> 

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