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On an open problem of Guo-Skiba |
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| Authors: | Zhenfeng Wu Wenbin Guo Baojun Li |
| Affiliation: | 1. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China2. College of Applied Mathematics, Chengdu University of information Technology, Chengdu 610225, China |
| Abstract: | Let G be a finite group, and let A be a proper subgroup of G. Then any chief factor H/A G of G is called a G-boundary factor of A. For any Gboundary factor H/A G of A, the subgroup (A ∩ H)/A G of G/ A G 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 |
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