1############################################################################ 2## 3## samples.g CRISP Burkhard Höfling 4## 5## Copyright © 2000, 2016 Burkhard Höfling 6## 7if not IsBound(InfoTest) then 8 DeclareInfoClass("InfoTest"); 9fi; 10SetInfoLevel(InfoTest,3); 11if not IsBound(PRINT_METHODS) then 12 PRINT_METHODS := false; 13fi; 14 15groups:= [ 16 function( ) 17 local G; 18 G := TrivialGroup( IsPcGroup); 19 SetName(G, "trivial pc group"); 20 return G; 21 end, 22 function( ) 23 local G; 24 G := TrivialGroup( IsPermGroup); 25 SetName(G, "trivial perm group"); 26 return G; 27 end, 28 function( ) 29 local G; 30 G := Group([], IdentityMat(4, GF(25))); 31 SetName(G, "trivial mat group"); 32 return G; 33 end, 34 function( ) 35 local G; 36 G := SmallGroup(48,29); 37 SetName(G, "GL(2,3) as pc group"); 38 return G; 39 end, 40 function( ) 41 local G; 42 G := SymmetricGroup( 4 ); 43 SetName(G, "Sym(4)"); 44 return G; 45 end, 46 function( ) 47 local G; 48 G := DihedralGroup( 10 ); 49 SetName(G, "Dih(10)"); 50 return G; 51 end, 52 function( ) 53 local G; 54 G := GL( 2, 3 ); 55 SetName(G, "GL(2,3)"); 56 return G; 57 end, 58 function( ) 59 local G; 60 G := FibonacciGroup( 3, 5 ); 61 SetName(G, "Fib(3,5) = C2 x C11"); 62 return G; 63 end, 64 function( ) 65 local G; 66 G := AutomorphismGroup(AlternatingGroup(4)); 67 SetName(G, "Aut(Alt(4)) = Sym(4)"); 68 return G; 69 end, 70 function( ) 71 local G; 72 G := DirectProduct(CyclicGroup(2), CyclicGroup(3), SymmetricGroup(4)); 73 SetName(G, "C2 x C3 x S4"); 74 return G; 75 end 76]; 77 78groups := groups{[1..Length(groups)-3]}; 79 80insolvgroups:= [ function( ) 81 return SymmetricGroup( 5 ); 82 end, 83 function( ) 84 return GL(2,5); 85 end, 86 function( ) 87 local G; 88 G := WreathProduct(CyclicGroup(IsPermGroup, 5), SymmetricGroup(5)); 89 SetName(G, "C5 wr S5"); 90 return G; 91 end, 92 function( ) 93 local G; 94 G := AutomorphismGroup(AbelianGroup([5,5])); 95 SetName(G, "Aut(C5xC5)"); 96 return G; 97 end]; 98 9925grps := PiGroups([2,5]); 100 101 102classes := function() 103 local cl, C; 104 cl := []; 105 106 C := SchunckClass(rec(bound := BoundaryFunction(25grps))); 107 SetName(C, "[2,5]-grps by boundary"); 108 Add(cl, C); 109 C := SaturatedFormation(rec(locdef := LocalDefinitionFunction(25grps))); 110 SetName(C, "[2,5]-grps by locdef"); 111 Add(cl, C); 112 C := GroupClass(rec(\in := MemberFunction(25grps))); 113 SetName(C, "[2,5]-grps by membersip"); 114 Add(cl, C); 115 C := OrdinaryFormation(rec( 116 res := function(G) 117 local pi; 118 pi := Difference(PrimeDivisors(Size(G)), [2,5]); 119 return NormalClosure(G, HallSubgroup(G, pi)); 120 end)); 121 SetName(C, "[2,5]-grps by res"); 122 Add(cl, C); 123 C := FittingClass(rec(rad := G -> Core(G, HallSubgroup(G, [2,5])))); 124 SetName(C, "[2,5]-grps by rad"); 125 Add(cl, C); 126 C := FittingClass(rec(inj := InjectorFunction(25grps))); 127 SetName(C, "[2,5]-grps by inj"); 128 Add(cl, C); 129 C := SchunckClass(rec(proj:= ProjectorFunction(25grps))); 130 SetName(C, "[2,5]-grps by proj"); 131 Add(cl, C); 132 return cl; 133end; 134 135 136############################################################################ 137## 138#E 139## 140