2.3 SubgroupViaStrings

SubgroupViaStrings( G , elstring, map )

Let G be a finitely presented group and elstring a string representing a list of words w₁, ..., w_n in the string generators of G. map should be a string containing every string generator of G as printed out by the procedure FpGroupViaStrings. SubgroupViaStrings returns the subgroup U generated by w₁, ..., w_n with parent group G elstring should be a string of the form "w₁,w₂, ... ,w_n" with w_i a word in the string generators of G.

    gap> cox := "a3b5c3d3e4c";;
    gap> rel := "a=(ce)^2" ;;
    gap> extrarel := "_PCE,(abc)^5,(bcd)^5";;
    gap> m11 := FpGroupViaStrings( cox, rel, extrarel );;
    && The map is: "abcde"
    gap> map := "abcde";;
    gap> a6 := SubgroupViaStrings( m11, "b,c,d,d^(abcbae)", map );
    Subgroup( M11, 
    [ f.2, f.3, f.4, f.5^-1*f.1^-1*f.2^-1*f.3^-1*f.2^-1*f.1^-1*f.4*f\
    .1*f.2*f.3*f.2*f.1*f.5 ] )
    gap> OperationCosetsFpGroup( m11, a6 );
    Group( ( 1, 2)( 3, 5)( 6, 9)(10,15)(11,16)(17,19)(18,20)(21,22),
    ( 2, 4)( 5, 8)( 7,11)( 9,14)(10,15)(12,17)(13,18)(21,22),
    ( 3, 5)( 4, 7)( 6,10)( 8,13)( 9,15)(11,16)(17,21)(19,22),
    ( 3, 6)( 5, 9)( 7,12)( 8,14)(10,15)(11,17)(16,19)(21,22),
    ( 1, 3)( 2, 5)( 4, 8)( 7,13)(10,15)(11,18)(16,20)(21,22) )