An Adjacency Criterion for the Prime Graph of a Finite Simple Group
Algebra i logika, Tome 44 (2005) no. 6, pp. 682-725
Voir la notice de l'article provenant de la source Math-Net.Ru
For every finite non-Abelian simple group, we give an exhaustive arithmetic criterion for adjacency of vertices in a prime graph of the group. For the prime graph of every finite simple group, this criterion is used to determine an independent set with a maximal number of vertices and an independent set with a maximal number of vertices containing 2, and to define orders on these sets; the information obtained is collected in tables. We consider several applications of these results to various problems in finite group theory, in particular, to the recognition-by-spectra problem for finite groups.
Keywords:
finite group, finite simple group, group of Lie type, spectrum of a finite group, recognition by spectrum, prime graph of a finite group, independence number of a prime graph, 2-independence number of a prime graph.
@article{AL_2005_44_6_a2,
author = {A. V. Vasil'ev and E. P. Vdovin},
title = {An {Adjacency} {Criterion} for the {Prime} {Graph} of {a~Finite} {Simple} {Group}},
journal = {Algebra i logika},
pages = {682--725},
publisher = {mathdoc},
volume = {44},
number = {6},
year = {2005},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/AL_2005_44_6_a2/}
}
A. V. Vasil'ev; E. P. Vdovin. An Adjacency Criterion for the Prime Graph of a Finite Simple Group. Algebra i logika, Tome 44 (2005) no. 6, pp. 682-725. http://geodesic.mathdoc.fr/item/AL_2005_44_6_a2/