mkdotl man page

mkdotl — find dotted lines between submodules


mkdotl [Options] <Name>


This program calculates a set of dotted lines between the local submodules. More precisely, it computes one dotted line for each submodule with head isomorphic to S⊕S, S irreducible. It can be shown that this set of dotted lines is sufficient to determine the complete submodule lattice as described by Benson and Conway.

Inputs for this program are the incidence matrix calculated by mkinc(1) and the cyclic submodules from mkcycl(1). Again, the whole calculation takes place in the condensed modules, so there is no need to uncondense the cyclic submodules.

It is known that all dotted lines have length q+1, where q is the order of the splitting field. This information is used by the program to determine if a dotted line is complete.

A list of all dotted lines is written to Name.dot.

Using the option --nodup eliminates redundant dotted lines from the output. If this option is specified, the program will calculate, for each dotted line, the maximal mountains contained in the span of the dotted line. If a dotted line has the same set of maximal mountains as an earlier dotted line, it is considered as redundant and dropped. Note that --nodup increases both memory and CPU time usage. However, the subsequent step, mkgraph(1), will benefit from a reduction of the number of dotted lines.


Quiet, no messages.
Verbose, more messages.
-T <MaxTime>
Set CPU time limit
Produce output in GAP format. This option implies -Q.
Eliminate redundant dotted lines.

Input Files

Constituent info file.
Cyclic submodules, generated by mkcycl(1).
Incidence matrix generated by mkinc(1).
Mountain data from mkinc(1).

Output Files

Constituent info file.
Dotted lines.

See Also

mkcycl(1), mkgraph(1), mkinc(1)

Referenced By

mkcycl(1), mkgraph(1), mkinc(1), mksub(1).

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