23.1 FreeGroup

FreeGroup( n )
FreeGroup( n, string )
FreeGroup( name1, name2.. )

FreeGroup returns the free group on n generators. The generators are displayed as string.1, string.2, ..., string.n. If string is missing it defaults to "f". If string is the name of the variable that you use to refer to the group returned by FreeGroup you can also enter the generators as string.i.

    gap> F2 := FreeGroup( 2, "A5" );;
    gap> A5 := F2 / [ F2.1^2, F2.2^3, (F2.1*F2.2)^5 ];
    Group( A5.1, A5.2 )
    gap> Size( A5 );
    60
    gap> F2 := FreeGroup( "a", "b" );;
    gap> D8 := F2 / [ F2.1^4, F2.2^2, F2.1^F2.2 / F2.1 ];
    Group( a, b )
    gap> a := D8.1;;  b := D8.2;;
    gap> Index( D8, Subgroup( D8, [ a ] ) );
    2 

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