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
|
#############################################################################
##
#W grppcfp.gd GAP library Bettina Eick
##
#Y Copyright (C) 1997, Lehrstuhl D fuer Mathematik, RWTH Aachen, Germany
#Y (C) 1998 School Math and Comp. Sci., University of St. Andrews, Scotland
#Y Copyright (C) 2002 The GAP Group
##
Revision.grppcfp_gd :=
"@(#)$Id: grppcfp.gd,v 4.15.2.1 2005/11/30 03:05:31 gap Exp $";
#############################################################################
##
#I InfoSQ
##
DeclareInfoClass( "InfoSQ" );
#############################################################################
##
#F PcGroupFpGroup( <G> )
##
## creates a PcGroup <P> from an FpGroup (see Chapter "Finitely Presented
## Groups") <G> whose presentation is polycyclic. The resulting group <P>
## has generators corresponding to the generators of <G>. They are printed
## in the same way as generators of <G>, but they lie in a different
## family. If the pc presentation of <G> is not confluent, an error message
## occurs.
#T should this become a method?
DeclareGlobalFunction( "PcGroupFpGroup" );
DeclareGlobalFunction( "PcGroupFpGroupNC" );
#############################################################################
##
#F InitEpimorphismSQ( F )
#F InitEpimorphismSQ(<hom>)
##
## If <F> is a finitiely presented group, this operation returns the SQ
## epimorphism system corresponding to the largest abelian quotient of <F>.
## If <hom> is a epimorphism from a finitely presented group to a pc
## group, it returns the system coresponding to this epimorphism.
## No argument checking is performed.
##
DeclareGlobalFunction( "InitEpimorphismSQ" );
#############################################################################
##
#F LiftEpimorphismSQ( epi, M, c )
##
## if c is an integer, split extensions are searched. if c=0 only one is
## returned, otherwise the subdirect product of all such extensions is
## found.
DeclareGlobalFunction( "LiftEpimorphismSQ" );
#############################################################################
##
#F BlowUpCocycleSQ( v, K, F )
##
DeclareGlobalFunction( "BlowUpCocycleSQ" );
#############################################################################
##
#F TryModuleSQ( epi, M )
##
DeclareGlobalFunction( "TryModuleSQ" );
#############################################################################
##
#F TryLayerSQ( epi, layer )
##
DeclareGlobalFunction( "TryLayerSQ" );
#############################################################################
##
#F SolvableQuotient(<F>,<size> )
#F SolvableQuotient(<F>,<primes> )
#F SolvableQuotient(<F>,<tuples> )
#F SQ(<F>,<...> )
##
## This routine calls the solvable quotient algorithm for a finitely
## presented group <F>. The quotient to be found can be specified in the
## following ways: Specifying an integer <size> finds a quotient of size up
## to <size> (if such large quotients exist). Specifying a list of primes
## in <primes> finds the largest quotient involving the given primes.
## Finally <tuples> can be used to prescribe a chief series.
##
## `SQ' can be used as a synonym for `SolvableQuotient'.
##
DeclareGlobalFunction( "SolvableQuotient" );
DeclareSynonym( "SQ", SolvableQuotient);
#############################################################################
##
#F EpimorphismSolvableQuotient(<F>,<param>)
##
## computes an epimorphism from the finitely presented group <fpgrp> to the
## largest solvable quotient given by <param> (specified as in
## `SolvableQuotient').
##
DeclareGlobalFunction("EpimorphismSolvableQuotient");
#############################################################################
##
#F AllModulesSQ( epi, M )
##
## returns a list of all permissible extensions of <epi> with the module
## <M>.
DeclareGlobalFunction("AllModulesSQ");
#############################################################################
##
#F EAPrimeLayerSQ( epi, prime )
##
## returns the largest elementary abelian <prime> layer extending <epi>.
DeclareGlobalFunction("EAPrimeLayerSQ");
|
