/usr/share/gap/lib/gpprmsya.gd is in gap-libs 4r6p5-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 | #############################################################################
##
#W gpprmsya.gd GAP Library Frank Celler
#W Alexander Hulpke
##
##
#Y Copyright (C) 1996, Lehrstuhl D für Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
## This file contains the declarations for symmetric and alternating
## permutation groups
##
#############################################################################
##
#P IsNaturalSymmetricGroup( <group> )
#P IsNaturalAlternatingGroup( <group> )
##
## <#GAPDoc Label="IsNaturalSymmetricGroup">
## <ManSection>
## <Prop Name="IsNaturalSymmetricGroup" Arg='group'/>
## <Prop Name="IsNaturalAlternatingGroup" Arg='group'/>
##
## <Description>
## A group is a natural symmetric or alternating group if it is
## a permutation group acting as symmetric or alternating group,
## respectively, on its moved points.
## <P/>
## For groups that are known to be natural symmetric or natural alternating
## groups, very efficient methods for computing membership,
## conjugacy classes, Sylow subgroups etc. are used.
## <P/>
## <Example><![CDATA[
## gap> g:=Group((1,5,7,8,99),(1,99,13,72));;
## gap> IsNaturalSymmetricGroup(g);
## true
## gap> g;
## Sym( [ 1, 5, 7, 8, 13, 72, 99 ] )
## gap> IsNaturalSymmetricGroup( Group( (1,2)(4,5), (1,2,3)(4,5,6) ) );
## false
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsNaturalSymmetricGroup", IsPermGroup );
DeclareProperty( "IsNaturalAlternatingGroup", IsPermGroup );
#############################################################################
##
#P IsAlternatingGroup( <group> )
##
## <#GAPDoc Label="IsAlternatingGroup">
## <ManSection>
## <Prop Name="IsAlternatingGroup" Arg='group'/>
##
## <Description>
## is <K>true</K> if the group <A>group</A> is isomorphic to a
## alternating group.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsAlternatingGroup", IsGroup );
#############################################################################
##
#M IsAlternatingGroup( <nat-alt-grp> )
##
InstallTrueMethod( IsAlternatingGroup, IsNaturalAlternatingGroup );
#############################################################################
##
#P IsSymmetricGroup( <group> )
##
## <#GAPDoc Label="IsSymmetricGroup">
## <ManSection>
## <Prop Name="IsSymmetricGroup" Arg='group'/>
##
## <Description>
## is <K>true</K> if the group <A>group</A> is isomorphic to a
## symmetric group.
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareProperty( "IsSymmetricGroup", IsGroup );
#############################################################################
##
#M IsSymmetricGroup( <nat-sym-grp> )
##
InstallTrueMethod( IsSymmetricGroup, IsNaturalSymmetricGroup );
#############################################################################
##
#A SymmetricParentGroup( <grp> )
##
## <#GAPDoc Label="SymmetricParentGroup">
## <ManSection>
## <Attr Name="SymmetricParentGroup" Arg='grp'/>
##
## <Description>
## For a permutation group <A>grp</A> this function returns the symmetric
## group that moves the same points as <A>grp</A> does.
## <Example><![CDATA[
## gap> SymmetricParentGroup( Group( (1,2), (4,5), (7,8,9) ) );
## Sym( [ 1, 2, 4, 5, 7, 8, 9 ] )
## ]]></Example>
## </Description>
## </ManSection>
## <#/GAPDoc>
##
DeclareAttribute("SymmetricParentGroup",IsPermGroup);
#############################################################################
##
#A AlternatingSubgroup( <grp> )
##
## <ManSection>
## <Attr Name="AlternatingSubgroup" Arg='grp'/>
##
## <Description>
## returns the intersection of <A>grp</A> with the alternating group on the
## points moved by <A>grp</A>.
## </Description>
## </ManSection>
##
DeclareAttribute("AlternatingSubgroup",IsPermGroup);
#############################################################################
##
#A OrbitStabilizingParentGroup( <grp> )
##
## <ManSection>
## <Attr Name="OrbitStabilizingParentGroup" Arg='grp'/>
##
## <Description>
## returns the subgroup of <C>SymmetricParentGroup(<A>grp</A>)</C> which stabilizes
## the orbits of <A>grp</A> setwise. (So it is a direct product of wreath
## products of symmetric groups.) It is a natural supergroup for the
## normalizer.
## </Description>
## </ManSection>
##
DeclareAttribute("OrbitStabilizingParentGroup",IsPermGroup);
#############################################################################
##
#E
|