1mksub(1) User Commands mksub(1)
2
6 mksub - find submodules
7
9 mksub [OPTIONS] <Name>
10
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 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 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 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 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 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 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 m Mountains.
62 d Dotted lines.
64 i Incidence matrix.
66 e ".lat" and ".gra" files.
68 s Submodules.
70 r Radical series.
72 o Socle series.
74
76 -Q Quiet, no messages.
77 -V Verbose, more messages.
79 -T <MaxTime>
81 Set CPU time limit
82 -G Produce output in GAP format. This option implies -Q.
84 -b Find blocks.
86 -o <Fmt>
88 Output elements in format Fmt.
89 -n <Fmt>
91 Exclude elements in format Fmt.
92
94 Name.cfinfo
95 Constituent info file.
96 Name.inc
98 Incidence matrix generated by mkinc(1).
99 Name.dot
101 Dotted-lines generated by mkdotl(1).
102 Name.mnt
104 Mountain dimensions.
105
107 Name.cfinfo
108 Constituent info file.
109 Name.out
111 Submodule lattice.
112 Name.lat
114 Incidence matrix of the submodules (GAP).
115 Name.gra
117 Submodule lattice for mkgraph(1).
118
120 genmod(1), mkdotl(1), mkgraph, mkinc(1)
121MeatAxe 2.4.24 mksub(1)