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On the index complex of a maximal subgroup and the group-theoretic properties of a finite group

Author(s): Wang Xiaojing | Jiang Lining

Journal: Boletim da Sociedade Paranaense de Matemática
ISSN 0037-8712

Volume: 23;
Issue: 1-2;
Start page: 65;
Date: 2005;
Original page

Keywords: index complex | solvable groups | super-solvable groups | nilpotent groups.

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.
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