1##############################################################################
2##
3#W  issue9.tst                   GAP4 package `XMod'             Chris Wensley
4#W
5#Y  Copyright (C) 2018, Chris Wensley et al,
6#Y  School of Computer Science, Bangor University, U.K.
7##
8gap> START_TEST( "XMod package: issue9.tst" );
9gap> saved_infolevel_xmod := InfoLevel( InfoXMod );;
10gap> SetInfoLevel( InfoXMod, 0 );;
11
12gap> G := Group( (1,2,3), (2,3), (4,5,6), (5,6) );;
13gap> Ggens := GeneratorsOfGroup( G );;
14gap> R := Subgroup( G, [ (1,2,3)(4,5,6), (2,3)(5,6) ] );;
15gap> Rgens := GeneratorsOfGroup( R );;
16gap> t := GroupHomomorphismByImages( G, R, Ggens,
17>      [ (1,2,3)(4,5,6), (2,3)(5,6), (), () ] );
18[ (1,2,3), (2,3), (4,5,6), (5,6) ] -> [ (1,2,3)(4,5,6), (2,3)(5,6), (), () ]
19gap> h := GroupHomomorphismByImages( G, R, Ggens,
20>      [ (), (),  (1,2,3)(4,5,6), (2,3)(5,6) ] );
21[ (1,2,3), (2,3), (4,5,6), (5,6) ] -> [ (), (), (1,2,3)(4,5,6), (2,3)(5,6) ]
22gap> e := GroupHomomorphismByImages( R, G, Rgens, Rgens );;
23gap> C2 := PreCat1ByTailHeadEmbedding( t, h, e );
24[Group( [ (1,2,3), (2,3), (4,5,6), (5,6) ] )=>Group(
25[ (1,2,3)(4,5,6), (2,3)(5,6) ] )]
26gap> SetName( G, "s3s3" );; SetName( R, "s3d" );;
27gap> C2 := PreCat1ByTailHeadEmbedding( t, h, e );
28[s3s3=>s3d]
29gap> X2 := XModOfCat1Group(C2);
30xmod([s3s3=>s3d])
31gap> Display( X2 );
32
33Crossed module xmod([s3s3=>s3d]) :-
34: Source group has generators:
35  [ (4,5,6), (5,6) ]
36: Range group has generators:
37  [ (1,2,3)(4,5,6), (2,3)(5,6) ]
38: Boundary homomorphism maps source generators to:
39  [ (1,2,3)(4,5,6), (2,3)(5,6) ]
40: Action homomorphism maps range generators to automorphisms:
41  (1,2,3)(4,5,6) --> { source gens --> [ (4,5,6), (4,6) ] }
42  (2,3)(5,6) --> { source gens --> [ (4,6,5), (5,6) ] }
43  These 2 automorphisms generate the group of automorphisms.
44: associated cat1-group is [s3s3=>s3d]
45
46gap> A2 := AutomorphismPermGroup( X2 );
47Group([ (1,3,2)(4,6,5)(7,9,8), (2,3)(5,6)(8,9) ])
48
49gap> SetInfoLevel( InfoXMod, saved_infolevel_xmod );;
50gap> STOP_TEST( "issue9.tst", 10000 );
51
52#############################################################################
53##
54#E  issue9.tst  . . . . . . . . . . . . . . . . . . . . . . . . . . ends here
55