Returns true if and only if the underlying concrete group elements for u and v are equal.
Returns true if and only if the underlying concrete group elements for u and v are not equal.
The parent group G of the element u.
The concrete group element corresponding to the BB-group element u.
The order of the underlying concrete group element of u.
> m24_standard := function(B) > repeat a := PseudoRandom(B); until Order(a) eq 10; > a := a ^ 5; > repeat b := PseudoRandom(B); until Order(b) eq 15; > b := b ^ 5; > repeat b := b ^ PseudoRandom(B); ab := a*b; > until Order(ab) eq 23; > x := ab*(ab^2*b)^2*ab*b; > if Order(x) eq 5 then b := b^-1; end if; > return a,b; > end function;We take a group which must be M24 and find these generators.
> G := PermutationGroup<24 | > [ 20, 4, 10, 3, 15, 9, 7, 1, 11, 22, 21, 19, 8, 2, 24, 5, > 12, 18, 13, 16, 14, 23, 6, 17 ], > [ 12, 18, 3, 2, 7, 11, 5, 21, 19, 22, 23, 1, 14, 17, 10, > 8, 4, 13, 24, 20, 9, 15, 6, 16 ]>; > #G; 244823040 > Transitivity(G); 5 > B := NaturalBlackBoxGroup(G); > a,b := m24_standard(B); a,b; GrpBBElt (1, 16)(2, 22)(3, 14)(4, 15)(5, 11)(6, 24)(7, 10)(8, 18)(9, 19)(12, 17)(13, 20)(21, 23) GrpBBElt (1, 14, 17)(2, 18, 13)(5, 16, 20)(7, 22, 9)(8, 24, 15)(19, 23, 21)The printing of the GrpBBElts shows the underlying concrete group elements. These may be extracted using the UnderlyingElement intrinsic for use within G.