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