This file is indexed.

/usr/share/gap/lib/grppcext.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
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
#############################################################################
##
#W  grppcext.gd                 GAP library                      Bettina Eick
##
#Y  Copyright (C)  1997,  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
##

#############################################################################
##
#I  InfoCompPairs
#I  InfoExtReps
##
DeclareInfoClass( "InfoCompPairs" );
DeclareInfoClass( "InfoExtReps");

#############################################################################
##
#F  MappedPcElement( <elm>, <pcgs>, <list> )
##
##  <ManSection>
##  <Func Name="MappedPcElement" Arg='elm, pcgs, list'/>
##
##  <Description>
##  returns the image of <A>elm</A> when mapping the pcgs <A>pcgs</A> onto <A>list</A>
##  homomorphically.
##  </Description>
##  </ManSection>
##
DeclareGlobalFunction("MappedPcElement");

#############################################################################
##
#F  ExtensionSQ( <C>, <G>, <M>, <c> )
##
##  <ManSection>
##  <Func Name="ExtensionSQ" Arg='C, G, M, c'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareGlobalFunction( "ExtensionSQ" );

#############################################################################
##
#F  FpGroupPcGroupSQ( <G> )
##
##  <ManSection>
##  <Func Name="FpGroupPcGroupSQ" Arg='G'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareGlobalFunction( "FpGroupPcGroupSQ" );

#############################################################################
##
#F  EXPermutationActionPairs( <D> )
##
##  <ManSection>
##  <Func Name="EXPermutationActionPairs" Arg='D'/>
##
##  <Description>
##  Let <A>D</A> be a direct product of automorphism group and matrix group as
##  used by <C>CompatiblePairs</C>. This function calculates a faithful
##  permutation representation of <A>D</A>, which can be used to speed up
##  stabilizer calculations. It returns a record with components <C>pairgens</C>:
##  Generators of <A>D</A>, <C>permgens</C>: corresponding permutations, <C>permgroup</C>:
##  the group generated by <C>permgens</C>, <C>isomorphism</C>: An isomorphism from
##  the permutation group to <A>D</A>. This isomorphism can be used to map
##  permutations, but it would be hard to get the preimage of a pair in <A>D</A>
##  as a permutation.
##  The routine may return  <K>false</K> if somehow such a representation could
##  not be found.
##  </Description>
##  </ManSection>
##
DeclareGlobalFunction( "EXPermutationActionPairs" );

#############################################################################
##
#F  EXReducePermutationActionPairs( <r> )
##
##  <ManSection>
##  <Func Name="EXReducePermutationActionPairs" Arg='r'/>
##
##  <Description>
##  Let <A>r</A> be a record as returned by <C>EXPermutationActionPairs</C>. This
##  function tries to reduce the underlying permutation representation (and
##  changes the record accordingly). It is of use when stepping to a
##  subgroup of all pairs.
##  </Description>
##  </ManSection>
##
DeclareGlobalFunction( "EXReducePermutationActionPairs" );

#############################################################################
##
#F  CompatiblePairs( <G>, <M>[, <D>] )
##
##  <#GAPDoc Label="CompatiblePairs">
##  <ManSection>
##  <Func Name="CompatiblePairs" Arg='G, M[, D]'/>
##
##  <Description>
##  returns the group of compatible pairs of the group <A>G</A> with the 
##  <A>G</A>-module <A>M</A> as subgroup of the direct product
##  Aut(<A>G</A>) <M>\times</M> Aut(<A>M</A>).
##  Here Aut(<A>M</A>) is considered as subgroup of a general linear group.
##  The optional argument <A>D</A> should be a subgroup of
##  Aut(<A>G</A>) <M>\times</M> Aut(<A>M</A>).
##  If it is given, then only the compatible pairs in <A>D</A> are computed.
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareGlobalFunction( "CompatiblePairs" );

#############################################################################
##
#O  Extension( <G>, <M>, <c> )
#O  ExtensionNC( <G>, <M>, <c> )
##
##  <#GAPDoc Label="Extension">
##  <ManSection>
##  <Oper Name="Extension" Arg='G, M, c'/>
##  <Oper Name="ExtensionNC" Arg='G, M, c'/>
##
##  <Description>
##  returns the extension of <A>G</A> by the <A>G</A>-module <A>M</A>
##  via the cocycle <A>c</A> as pc groups.
##  The <C>NC</C> version does not check the resulting group for consistence.
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareOperation( "Extension", [ CanEasilyComputePcgs, IsObject, IsVector ] );
DeclareOperation( "ExtensionNC", [ CanEasilyComputePcgs, IsObject, IsVector ] );

#############################################################################
##
#O  Extensions( <G>, <M> )
##
##  <#GAPDoc Label="Extensions">
##  <ManSection>
##  <Oper Name="Extensions" Arg='G, M'/>
##
##  <Description>
##  returns all extensions of <A>G</A> by the <A>G</A>-module <A>M</A>
##  up to equivalence as pc groups.
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareOperation( "Extensions", [ CanEasilyComputePcgs, IsObject ] );

#############################################################################
##
#O  ExtensionRepresentatives( <G>, <M>, <P> )
##
##  <#GAPDoc Label="ExtensionRepresentatives">
##  <ManSection>
##  <Oper Name="ExtensionRepresentatives" Arg='G, M, P'/>
##
##  <Description>
##  returns all extensions of <A>G</A> by the <A>G</A>-module <A>M</A> up to
##  equivalence under action of <A>P</A> where <A>P</A> has to be a subgroup
##  of the group of compatible pairs of <A>G</A> with <A>M</A>.
##  <Example><![CDATA[
##  gap> G := SmallGroup( 4, 2 );;
##  gap> mats := List( Pcgs( G ), x -> IdentityMat( 1, GF(2) ) );;
##  gap> M := GModuleByMats( mats, GF(2) );;
##  gap> A := AutomorphismGroup( G );;
##  gap> B := GL( 1, 2 );;
##  gap> D := DirectProduct( A, B );
##  <group of size 6 with 4 generators>
##  gap> P := CompatiblePairs( G, M, D );
##  <group of size 6 with 2 generators>
##  gap> ExtensionRepresentatives( G, M, P );
##  [ <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators> ]
##  gap> Extensions( G, M );
##  [ <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators>, 
##    <pc group of size 8 with 3 generators> ]
##  ]]></Example>
##  </Description>
##  </ManSection>
##  <#/GAPDoc>
##
DeclareOperation( "ExtensionRepresentatives", 
                    [CanEasilyComputePcgs, IsObject, IsObject] );

#############################################################################
##
#O  SplitExtension( <G>, <M> )
#O  SplitExtension( <G>, <aut>, <N> )
##
##  <ManSection>
##  <Oper Name="SplitExtension" Arg='G, M'/>
##  <Oper Name="SplitExtension" Arg='G, aut, N'/>
##
##  <Description>
##  returns the split extension of <A>G</A> by the <A>G</A>-module <A>M</A>. In the second
##  form it returns the split extension of <A>G</A> by the arbitrary finite group
##  <A>N</A> where <A>aut</A> is a homomorphism of <A>G</A> into Aut(<A>N</A>).
##  </Description>
##  </ManSection>
##
DeclareOperation( "SplitExtension", [CanEasilyComputePcgs, IsObject] );

#############################################################################
##
#O  TopExtensionsByAutomorphism( <G>, <aut>, <p> )
##
##  <ManSection>
##  <Oper Name="TopExtensionsByAutomorphism" Arg='G, aut, p'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareOperation( "TopExtensionsByAutomorphism",
                               [CanEasilyComputePcgs, IsObject, IsInt] );

#############################################################################
##
#O  CyclicTopExtensions( <G>, <p> )
##
##  <ManSection>
##  <Oper Name="CyclicTopExtensions" Arg='G, p'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareOperation( "CyclicTopExtensions", 
                       [CanEasilyComputePcgs, IsInt] );

#############################################################################
##
#A  SocleComplement(<G>)
##
##  <ManSection>
##  <Attr Name="SocleComplement" Arg='G'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareAttribute( "SocleComplement", IsGroup );

#############################################################################
##
#A  SocleDimensions(<G>)
##
##  <ManSection>
##  <Attr Name="SocleDimensions" Arg='G'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareAttribute( "SocleDimensions", IsGroup );

#############################################################################
##
#A  ModuleOfExtension( < G > );
##
##  <ManSection>
##  <Attr Name="ModuleOfExtension" Arg='G'/>
##
##  <Description>
##  </Description>
##  </ManSection>
##
DeclareAttribute( "ModuleOfExtension", IsGroup );


#############################################################################
##
#E