Follow-up Session

gap> G:= SymmetricGroup(6);
Sym( [ 1 .. 6 ] )
gap> a:= Random(G);
(1,6)(2,5,4,3)
gap> Order(a); Order(Inverse(a));
4
4
gap> a:= Random(G); Order(a); Order(Inverse(a));
(1,3,2,6)(4,5)
4
4
gap> a:= Random(G); Order(a); Order(Inverse(a));
(1,3,4,5,6)
5
5
gap> a:= Random(G); Order(a); Order(Inverse(a));
(1,6,2,5,3,4)
6
6
gap> a:= Random(G); Order(a); Order(Inverse(a));
(1,3,2,4,6)
5
5
gap> a:= Random(G); Order(a); Order(Inverse(a));
(1,4,3)(2,6,5)
3
3
gap> a:= Random(G); Order(a); Order(Inverse(a));
(1,5,6)(2,4,3)
3
3
gap> a:= Random(G); Order(a); b:= Random(G); Order(b); Order(a*b);
(1,6,2)(4,5)
6
(1,3,5,6)(2,4)
4
6
gap> a:= Random(G); Order(a); b:= Random(G); Order(b); Order(a*b);
(1,4,6)(2,3,5)
3
(1,2,3,6)(4,5)
4
4
gap> a:= Random(G); Order(a); b:= Random(G); Order(b); Order(a*b);
(1,4)(3,5,6)
6
(1,2)(3,5,4,6)
4
6
gap> a:= Random(G); Order(a); b:= Random(G); Order(b); Order(a*b);
(1,6)(2,5,3)
6
(2,4)(3,6)
2
6
gap> IsCyclic(DirectProduct( CyclicGroup(4), CyclicGroup(2)));
false
gap> IsCyclic(DirectProduct( CyclicGroup(4), CyclicGroup(5)));
true
gap> IsCyclic(DirectProduct( CyclicGroup(4), CyclicGroup(10)));
false
gap> IsCyclic(DirectProduct( CyclicGroup(3), CyclicGroup(10)));
true
gap> (2,3,4)^(1,4,2);
(1,3,2)
gap> (1,2,4)*(2,3,4)*(1,4,2);
(1,3,2)
gap> G:= Group((1,2,3,4));
Group([ (1,2,3,4) ])
gap> f:= GroupHomomorphismByImages(G, G, [(1,2,3,4)] , [(1,2,3,4)^()]);
[ (1,2,3,4) ] -> [ (1,2,3,4) ]
gap> f:= GroupHomomorphismByImages(G, G, [(1,2,3,4)] , [(1,2,3,4)^(1,2,3,4)]);
[ (1,2,3,4) ] -> [ (1,2,3,4) ]
gap> f:= GroupHomomorphismByImages(G, G, [(1,2,3,4)] , [(1,2,3,4)^(1,3)(2,4)]);
[ (1,2,3,4) ] -> [ (1,2,3,4) ]
gap> f:= GroupHomomorphismByImages(G, G, [(1,2,3,4)] , [(1,2,3,4)^(1,4,3,2)]);
[ (1,2,3,4) ] -> [ (1,2,3,4) ]
gap> G: SymmetricGroup(3);
Syntax error: ; expected
G: SymmetricGroup(3);
 ^
Sym( [ 1 .. 3 ] )
gap> G:= SymmetricGroup(3);
Sym( [ 1 .. 3 ] )
gap> f:= GroupHomomorphismByImages(G, G, [(1,2,3), (1,2)] , [(1,2,3)^(), (1,2)^()]);
[ (1,2,3), (1,2) ] -> [ (1,2,3), (1,2) ]
gap> f:= GroupHomomorphismByImages(G, G, [(1,2,3), (1,2)] , [(1,2,3)^(2,3), (1,2)^(2,3)]);
[ (1,2,3), (1,2) ] -> [ (1,3,2), (1,3) ]
gap> Read("groupact");
gap> groupact((1,2,3,4,5,6),(1,2));
[ () ]
gap> LogTo();