Weakly <em class="a-plus-plus">SS</em>-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group

  • Xirong Zhang
  • Tao Zhao School Sci., Shandong Univ. Technology, Zibo, China)

Abstract

A subgroup H is said to be an s-permutable subgroup of a finite group G provided that the equality HP =PH holds for every Sylow subgroup P of G. Moreover, H is called SS-quasinormal in G if there exists a supplement B of H to G such that H permutes with every Sylow subgroup of B. We show that H is weakly SS-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable and H \ T is SS-quasinormal in G. We study the influence of some weakly SS-quasinormal minimal subgroups on the nilpotency of a finite group G. Numerous results known from the literature are unified and generalized.
Published
25.02.2014
How to Cite
ZhangX., and ZhaoT. “Weakly <em class="a-Plus-plus">SS</Em&gt;-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, no. 2, Feb. 2014, pp. 187–194, http://umj.imath.kiev.ua/index.php/umj/article/view/2122.
Section
Research articles