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Title

PARTIALLYS-EMBEDDED MINIMAL SUBGROUPS OF FINITE GROUPS

Writers

ZHAO TAO | ZHANG QINGLIANG

Pages

 Start Page 7 | End Page 16

Abstract

 Suppose that H is a subgroup of G, then H is said to be s-permutable in G, if H permutes with every Sylow subgroup of G. If HP=PH hold for every Sylow subgroup P of G with (|Pj|, |jHj|) = 1), then H is called an s-semipermutable subgroup of G. In this paper, we say that H is partially S-embedded in G if G has a normal subgroup T such that HT is s-permutable in G and H  Ç T £ H s-G, where H s-G is generated by all s-semipermutable subgroups of G contained in H. We investigate the influence of some partiallyS-embedded minimal subgroups on the nilpotency and supersolubility of a finite group G. A series of known results in the literature are unified and generalized.

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