On partially conjugate-permutable subgroups of finite groups

2012/06/01 by V. I. Murashka, Murashka, V. I., A. F. Vasil'ev +1
Mathematics · #FOS: Mathematics #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1206.0185

arxiv created 2012/06/01 · arxiv updated 2012/06/04

Abstract

Let R be a subset of a group G. We call a subgroup H of G the R-conjugate-permutable subgroup of G, if HH^x=H^xH for all x∈ R. This concept is a generalization of conjugate-permutable subgroups introduced by T. Foguel. Our work focuses on the influence of R-conjugate-permutable subgroups on the structure of finite groups in case when R is the Fitting subgroup or its generalizations F^*(G) (introduced by H. Bender in 1970) and F(G) (introduced by P. Shmid 1972). We obtain a new criteria for nilpotency and supersolubility of finite groups which generalize some well known results.

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