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THE INFLUENCE OF Φ-S-SUPPLEMENTED SUBGROUPS ON THE STRUCTURE OF FINITE GROUPS

CHANGWEN LI

School of Mathematical Science, Jiangsu Normal University, Xuzhou 221116, P. R. China

https://doi.org/10.1142/S0219498812500648Cited by:2 (Source: Crossref)

Abstract

A subgroup H of a group G is called Φ-s-supplemented in G if there exists a subnormal subgroup K of G such that G = HK and H ∩ K ≤ Φ (H), where Φ(H) is the Frattini subgroup of H. We investigate the influence of Φ-s-supplemented subgroups on the p-nilpotency, p-supersolvability and supersolvability of finite groups.

Keywords:

AMSC: 20D10, 20D20

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