On the index complex of a maximal subgroup and the group-theoretic properties of a finite group - doi: 10.5269/bspm.v23i1-2.7458

Lining Jiang; Wang Xiaojing

doi:10.5269/bspm.v23i1-2.7458

On the index complex of a maximal subgroup and the group-theoretic properties of a finite group - doi: 10.5269/bspm.v23i1-2.7458

Auteurs-es

Lining Jiang Beijing Institute of Technology
Wang Xiaojing Beijing Institute of Civil Eng. and Arch.

DOI :

https://doi.org/10.5269/bspm.v23i1-2.7458

Mots-clés :

index complex, solvable groups, super-solvable groups, nilpotent groups.

Résumé

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.