Finite Groups with Given Weakly σ-Permutable Subgroups
- 作者: Cao C.1, Wu Z.1, Guo W.1
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隶属关系:
- Department of Mathematics
- 期: 卷 59, 编号 1 (2018)
- 页面: 157-165
- 栏目: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/171705
- DOI: https://doi.org/10.1134/S0037446618010172
- ID: 171705
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Let G be a finite group and let σ = {σi | i ∈ I} be a partition of the set of all primes P. A set ℋ of subgroups of G is said to be a complete Hall σ-set of G if each nonidentity member of ℋ is a Hall σi-subgroup of G and ℋ has exactly one Hall σi-subgroup of G for every σi ∈ σ(G). A subgroup H of G is said to be σ-permutable in G if G possesses a complete Hall σ-set ℋ such that HAx = AxH for all A ∈ ℋ and all x ∈ G. A subgroup H of G is said to be weakly σ-permutable in G if there exists a σ-subnormal subgroup T of G such that G = HT and H ∩ T ≤ HσG, where HσG is the subgroup of H generated by all those subgroups of H which are σ-permutable in G. We study the structure of G under the condition that some given subgroups of G are weakly σ-permutable in G. In particular, we give the conditions under which a normal subgroup of G is hypercyclically embedded. Some available results are generalized.
作者简介
C. Cao
Department of Mathematics
编辑信件的主要联系方式.
Email: cccao@mail.ustc.edu.cn
中国, Hefei
Z. Wu
Department of Mathematics
Email: cccao@mail.ustc.edu.cn
中国, Hefei
W. Guo
Department of Mathematics
Email: cccao@mail.ustc.edu.cn
中国, Hefei