25.47 NextModuleSQ

NextModuleSQ( s, M )

Let S be an SQ record describing a finite solvable quotient Q of a finitely presented group G. NextModuleSQ tries to extend Q by the module M such that the extension is still a quotient of G

    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 >>
    gap> m := ModulesSQ( s, GF(3) );;
    gap> NextModuleSQ( s, m[1] );
    << solvable quotient of size 2^2 >>
    gap> NextModuleSQ( s, m[2] );
    << solvable quotient of size 2^2*3 >>
    gap> NextModuleSQ( s, m[3] );
    << solvable quotient of size 2^2 >>
    gap> NextModuleSQ( s, m[4] );
    << solvable quotient of size 2^2*3 >> 

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