gap> 
gap> U:=( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19);
( 1, 3, 8, 6)( 2, 5, 7, 4)( 9,33,25,17)(10,34,26,18)(11,35,27,19)
gap> L:=( 9,11,16,14)(10,13,15,12)( 1,17,41,40)( 4,20,44,37)( 6,22,46,35);
( 1,17,41,40)( 4,20,44,37)( 6,22,46,35)( 9,11,16,14)(10,13,15,12)
gap> F:= (17,19,24,22)(18,21,23,20)( 6,25,43,16)( 7,28,42,13)( 8,30,41,11);
( 6,25,43,16)( 7,28,42,13)( 8,30,41,11)(17,19,24,22)(18,21,23,20)
gap> R:=(25,27,32,30)(26,29,31,28)( 3,38,43,19)( 5,36,45,21)( 8,33,48,24);
( 3,38,43,19)( 5,36,45,21)( 8,33,48,24)(25,27,32,30)(26,29,31,28)
gap> B:=(33,35,40,38)(34,37,39,36)( 3, 9,46,32)( 2,12,47,29)( 1,14,48,27);
( 1,14,48,27)( 2,12,47,29)( 3, 9,46,32)(33,35,40,38)(34,37,39,36)
gap> D:=(41,43,48,46)(42,45,47,44)(14,22,30,38)(15,23,31,39)(16,24,32,40);
(14,22,30,38)(15,23,31,39)(16,24,32,40)(41,43,48,46)(42,45,47,44)
gap> 
gap> square_group := Group(U^2,L^2,F^2,R^2,B^2,D^2);;
gap> g1:=(2,42)(34,23);
( 2,42)(23,34)
gap> 
gap> ans:=g1 in square_group;
false
gap> g1:=(2,23)(34,42);
( 2,23)(34,42)
gap> ans:=g1 in square_group;
false
gap> g1:=(2,42)(34,23);
( 2,42)(23,34)
gap> g1:=(2,42)(34,23)(4,5)(26,10);
( 2,42)( 4, 5)(10,26)(23,34)
gap> ans:=g1 in square_group;
true
gap> Read("d:/gap/gap3r4p3/lib/abstab.g");
The record 'descriptions' contains brief descriptions of the functions
in this file.
Functions of importance: MakeAbStabChain, FactorPermGroupElement, Shrink
gap> 
gap> g2:=FactorPermGroupElement(square_group,g1);
g1*g2*g1^-1*g6*g1*g2*g1^-1*g4^-1*g6*g1*g3*g2^-1*g4^-1*g3^-1*g2*g3^-1*g2*g3*g2^\
-1*g4*g2*g3^-1*g1^-1*g6^-1*g4*g1*g2^-1*g1^-1*g6^-1*g1*g2^-1*g3*g2^-1*g4^-1*g3^\
-1*g1*g3*g2^-1*g4^-1*g3^-1*g1*g3*g2^-1*g4^-1*g3^-1*g2*g3^-1*g2*g3*g2^-1*g4*g2*\
g3^-1*g1^-1*g3*g4*g2*g3^-1*g1^-1*g3*g4*g2*g3^-1*g2*g1^-1*g6*g1*g2*g1^-1*g4^-1*\
g6*g1*g3*g2^-1*g4^-1*g2*g3^-1*g2^-1*g3*g2^-1*g3*g4*g2*g3^-1*g1^-1*g6^-1*g4*g1*\
g2^-1*g1^-1*g6^-1*g1*g2^-1*g1^-1
gap> g3:=Shrink(square_group,g2);
g2^-1*g1^-1*g3^-1*g2^-1*g3^-1*g2^-1*g3*g2^-1*g1^-1*g2^-1
gap> g4:=Shrink(square_group,g3);
g2^-1*g1^-1*g3^-1*g2^-1*g3^-1*g2^-1*g3*g2^-1*g1^-1*g2^-1
gap> FactorPermGroupElement(square_group,U^2);
g1
gap> FactorPermGroupElement(square_group,L^2);
g2
gap> FactorPermGroupElement(square_group,F^2);
g3
gap> uu:=(1,3)(2,4);ff:=(1,8)(4,5);dd:=(5,7)(6,8);
(1,3)(2,4)
(1,8)(4,5)
(5,7)(6,8)
gap> bb:=(3,6)(2,7);rr:=(2,5)(1,6);ll:=(4,7)(3,8);
(2,7)(3,6)
(1,6)(2,5)
(3,8)(4,7)
gap> H:=Group(uu,ff,rr,dd,bb,ll);
Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), (3,8)
(4,7) )
gap> (1,3)(2,5) in H;
false
gap> (1,8)(2,5) in H;
false
gap> (1,6)(2,5) in H;
true
gap> (1,6)(3,8) in H;
true
gap> (1,3,6,8) in H;
false
gap> (1,6,3,8) in H;
false
gap> (1,8,3,6) in H;
false
gap> (1,8,6,3) in H;
false
gap> (1,3,8,6) in H;
false
gap> (1,6,8,3) in H;
false
gap> (2,4,4,7)(1,6,8,3) in H;
Error, Perm: cycles must be disjoint
Group( (1,3)(2,4), (1,8)(4,5), (1,6)(2,5), (5,7)(6,8), (2,7)(3,6), (3,8)
(4,7) )
gap> (2,4,5,7)(1,6,8,3) in H;
false
gap> (2,5,4,7)(1,6,8,3) in H;
false
gap> (2,5,7,4)(1,6,8,3) in H;
true
gap> h1:=(2,5,7,4)(1,6,8,3);
(1,6,8,3)(2,5,7,4)
gap> h2:=FactorPermGroupElement(square_group,h1);
Error, operations: product of character and word is not defined at
abelm := l[2] * abelm ... in
FactorPermGroupElement( square_group, h1 ) called from
main loop
brk> quit;
gap> h2:=FactorPermGroupElement(H,h1);
g6*g4*g3
gap> FactorPermGroupElement(H,uu);
g1
gap> FactorPermGroupElement(H,ff);
g2
gap> FactorPermGroupElement(H,dd);
g4
gap> FactorPermGroupElement(H,bb);
g5
gap> FactorPermGroupElement(H,rr);
g3
gap> FactorPermGroupElement(H,ll);
g6
gap> h1*g1;
( 1, 6, 8, 3)( 2, 4,42)( 5, 7)(10,26)(23,34)
gap> h1*h1;
(1,8)(2,7)(3,6)(4,5)
gap> h1^3;
(1,3,8,6)(2,4,7,5)
gap> h1^4;
()
gap> (1,3)(2,4) in H;
true
gap> h2:=(1,3)(2,4);
(1,3)(2,4)
gap> h1*h2;
(1,6,8)(2,5,7)
gap> h1;
(1,6,8,3)(2,5,7,4)
gap> h2:=(6,8)(5,7);
(5,7)(6,8)
gap> h1*h2;
(1,8,3)(2,7,4)
gap> h1*h2*h1;
(1,3,6,8)(2,4,5,7)
gap> h3:=h1*h2*h1;
(1,3,6,8)(2,4,5,7)
gap> h3^2;
(1,6)(2,5)(3,8)(4,7)
gap> h3^-1;
(1,8,6,3)(2,7,5,4)
gap> h2:=FactorPermGroupElement(H,h1);
g6*g4*g3
gap> quit;