1mksub(1)                         User Commands                        mksub(1)
2
3
4

NAME

6       mksub - find submodules
7

SYNOPSIS

9       mksub [OPTIONS] <Name>
10

DESCRIPTION

12       This  program  calculates the submodule lattice using the output gener‐
13       ated by mkinc(1) and mkdotl(1).  In this final step  no  matrix  opera‐
14       tions  are involved.  Instead the program works with bit strings repre‐
15       senting the incidences and dotted-lines.  The lattice may be decomposed
16       into blocks using the -b option (see below).
17
18       Submodules  are  calculated generation by generation, the first genera‐
19       tion consisting of all submodules generated by one local submodule.  In
20       the  nth  generation all submodules generated by a submodule of genera‐
21       tion n+1 local submodule are calculated.  If no more submodules appear,
22       the algorithm terminates.
23
24       Output  is  written to three text files and one binary file.  The first
25       file, Name.out, contains a list of irreducible constituents, the  inci‐
26       dence  matrix, the dimensions of all local submodules, a list of dotted
27       lines, a list of all submodules, the radical and socle  series,  and  a
28       list  of all mountains, i.e., local submodules.  The second output file
29       is Name.lat.  It contains the lattice as a list in  GAP  format.   This
30       list  contains,  for  each submodule, its dimension, maximal submodules
31       and isomorphism types of simple factors  are  given  (see  the  example
32       below).  The third output file, Name.gra, contains a description of the
33       submodule lattice together with some additional information.  This file
34       is read by the mkgraph program to produce a graphical representation of
35       the lattice.  A further output file, Name.sub, contains  the  submodule
36       lattice in binary format.  This file is read by the genmod(1) program.
37
38   BLOCKS
39       If  the -b option is used, mksub(1) tries to decompose the lattice into
40       blocks.  By definition, a block is a set of  one  or  more  composition
41       factors  which  is  closed under incidences of local submodules.  For a
42       decomposition into blocks to be possible, there must be direct summands
43       with no common irreducible constituent.  If a decomposition exists, the
44       whole lattice can be reconstructed from its blocks  by  forming  direct
45       sums.
46
47       Output  files  are  created  separately for each block, and a number is
48       appended to the name.  For example, if  the  representation  is  called
49       "psl277"  and  the lattice decomposes into 3 blocks, mksub(1) creates 9
50       output files:
51
52       psl211.out.1   psl211.lat.1   psl211.gra.1
53       psl211.out.2   psl211.lat.2   psl211.gra.2
54       psl211.out.3   psl211.lat.3   psl211.gra.3
55
56   CHANGING THE OUTPUT FORMAT
57       The default output as shown above  may  be  changed  by  using  the  -o
58       option.  The format is any combination of "m", "d", "i", "e", "s", "r",
59       and "o".  Each letter corresponds to a certain piece of output:
60
61       m      Mountains.
62
63       d      Dotted lines.
64
65       i      Incidence matrix.
66
67       e      ".lat" and ".gra" files.
68
69       s      Submodules.
70
71       r      Radical series.
72
73       o      Socle series.
74

OPTIONS

76       -Q     Quiet, no messages.
77
78       -V     Verbose, more messages.
79
80       -T <MaxTime>
81              Set CPU time limit
82
83       -G     Produce output in GAP format.  This option implies -Q.
84
85       -b     Find blocks.
86
87       -o <Fmt>
88              Output elements in format Fmt.
89
90       -n <Fmt>
91              Exclude elements in format Fmt.
92

INPUT FILES

94       Name.cfinfo
95              Constituent info file.
96
97       Name.inc
98              Incidence matrix generated by mkinc(1).
99
100       Name.dot
101              Dotted-lines generated by mkdotl(1).
102
103       Name.mnt
104              Mountain dimensions.
105

OUTPUT FILES

107       Name.cfinfo
108              Constituent info file.
109
110       Name.out
111              Submodule lattice.
112
113       Name.lat
114              Incidence matrix of the submodules (GAP).
115
116       Name.gra
117              Submodule lattice for mkgraph(1).
118

SEE ALSO

120       genmod(1), mkdotl(1), mkgraph, mkinc(1)
121
122
123
124MeatAxe                             2.4.24                            mksub(1)
Impressum