On c#-normal subgroups in finite groups

doi:10.1007/s11464-018-0724-x

Front. Math. China

2018, Vol. 13

Issue (5) : 1169-1178 https://doi.org/10.1007/s11464-018-0724-x

RESEARCH ARTICLE

On c^#-normal subgroups in finite groups

Huaquan WEI¹(

), Qiao DAI¹, Hualian ZHANG¹, Yubo LV¹, Liying YANG²(

)

¹. College of Mathematics and Information Sciences, Guangxi University, Nanning 530004, China
². School of Mathematics and Statistics, Guangxi Teachers Education University, Nanning 530023, China

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Abstract

A subgroup H of a finite group G is called a c^#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is a CAP-subgroup of G. In this paper, we investigate the influence of fewer c^#-normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results.

Keywords Finite group c^#-normal p-supersolvable p-nilpotent supersolvable

Corresponding Author(s): Huaquan WEI,Liying YANG

Issue Date: 29 October 2018

Cite this article:

Huaquan WEI,Qiao DAI,Hualian ZHANG, et al. On c^#-normal subgroups in finite groups[J]. Front. Math. China, 2018, 13(5): 1169-1178.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0724-x
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I5/1169

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