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- Title
A Note on HC-Subgroups of Finite Groups.
- Authors
Gao, Jinxin; Guo, Xiuyun
- Abstract
A subgroup H of a finite group G is said to be an H<inline-graphic></inline-graphic>-subgroup in G if NG(H)∩Hg≤H<inline-graphic></inline-graphic> for all g∈G<inline-graphic></inline-graphic>; we say that H is an HC<inline-graphic></inline-graphic>-subgroup in G if there is a normal subgroup T of G such that G=HT<inline-graphic></inline-graphic> and Hg∩NT(G)≤H<inline-graphic></inline-graphic> for all g∈G<inline-graphic></inline-graphic>. In this note, we obtain some interesting results by applying HC<inline-graphic></inline-graphic>-subgroups. As applications, many known results are generalized in recent literature.
- Subjects
FINITE groups; FRATTINI subgroups; GROUP theory; MAXIMAL subgroups; NILPOTENT groups
- Publication
Bulletin of the Iranian Mathematical Society, 2018, Vol 44, Issue 2, p505
- ISSN
1018-6301
- Publication type
Article
- DOI
10.1007/s41980-018-0034-9