Let G be a finite group. The table of marks of G arises from a
characterization of the permutation representations of G by certain
numbers of fixed points. It provides a compact description of the subgroup
lattice of G and enables explicit calculations in the Burnside ring of
G. In this article we introduce a method for constructing the table of
marks of G from tables of marks of proper subgroups of G. An
implementation of this method is available in the GAP language. These
computer programs are used to construct the table of marks of the sporadic
simple Mathieu group $M_{24}$. The final section describes how to derive
information about the structure of G from its table of marks via the
investigation of certain Möbius functions and the idempotents of the
Burnside ring of G. Tables with detailed
information about $M_{24}$ and other groups are included.
Publié le : 1997-05-14
Classification:
Burnside ring,
table of marks,
subgroup lattice,
Mathieu groups,
20D30,
20D08
@article{1047920424,
author = {Pfeiffer, G\"otz},
title = {The subgroups of {$M\sb {24}$}, or how to compute the table of marks of a finite group},
journal = {Experiment. Math.},
volume = {6},
number = {4},
year = {1997},
pages = { 247-270},
language = {en},
url = {http://dml.mathdoc.fr/item/1047920424}
}
Pfeiffer, Götz. The subgroups of {$M\sb {24}$}, or how to compute the table of marks of a finite group. Experiment. Math., Tome 6 (1997) no. 4, pp. 247-270. http://gdmltest.u-ga.fr/item/1047920424/