Let G be a finite group, S^p(G); \Phi'(G) and \Phi_1(G) be generalizations of the Frattini subgroup of G. Based on these characteristic subgroups and using Deskins index complex, this paper gets some necessary and suffcient conditions for G to be a p-solvable, \pi-solvable, solvable, super-solvable and nilpotent group.
@article{7458,
title = {On the index complex of a maximal subgroup and the group-theoretic properties of a finite group - doi: 10.5269/bspm.v23i1-2.7458},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {23},
year = {2009},
doi = {10.5269/bspm.v23i1-2.7458},
language = {EN},
url = {http://dml.mathdoc.fr/item/7458}
}
Jiang, Lining; Xiaojing, Wang. On the index complex of a maximal subgroup and the group-theoretic properties of a finite group - doi: 10.5269/bspm.v23i1-2.7458. Boletim da Sociedade Paranaense de Matemática, Tome 23 (2009) . doi : 10.5269/bspm.v23i1-2.7458. http://gdmltest.u-ga.fr/item/7458/