On an open problem of Guo-Skiba

doi:10.1007/s11464-016-0572-5

Front. Math. China

2016, Vol. 11

Issue (6) : 1603-1612 https://doi.org/10.1007/s11464-016-0572-5

RESEARCH ARTICLE

On an open problem of Guo-Skiba

Zhenfeng WU¹,Wenbin GUO¹(

),Baojun LI²

¹. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
². College of Applied Mathematics, Chengdu University of information Technology, Chengdu 610225, China

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Abstract

Let G be a finite group, and let A be a proper subgroup of G. Then any chief factor H/AG of G is called a G-boundary factor of A. For any Gboundary factor H/AG of A, the subgroup (A ∩ H)/AG of G/AG is called a G-trace of A. In this paper, we prove that G is p-soluble if and only if every maximal chain of G of length 2 contains a proper subgroup M of G such that either some G-trace of M is subnormal or every G-boundary factor of M is a p?-group. This result give a positive answer to a recent open problem of Guo and Skiba. We also give some new characterizations of p-hypercyclically embedded subgroups.

Keywords Finite group p-hypercyclically embedded subgroup G-boundary factor G-trace of subgroup meet-irreducible subgroup

Corresponding Author(s): Wenbin GUO

Issue Date: 18 October 2016

Cite this article:

Zhenfeng WU,Wenbin GUO,Baojun LI. On an open problem of Guo-Skiba[J]. Front. Math. China, 2016, 11(6): 1603-1612.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-016-0572-5
https://academic.hep.com.cn/fmc/EN/Y2016/V11/I6/1603

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