某些极大准素 σ_c -正规子群对群结构的影响

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中图分类号：0152.1 文献标志码：A 文章编号：1673-5072（2025）04-0376-05

Abstract： Let H≤G.A subgroup H G is said to be c -normal in finite group G ，if there exists a normal subgroup K d G such that G=HK and H∩K≤HG ，and is at the core H i G . Let P be a Sylow p -subgroups G .In order to investigate the influence some c -normal maximal subgroups P on the structure finite groups，comparing the previous conditions on all maximal subgroupsand considering the intersection the Sylow subgroup P and the p -module subgroup Op（G） ，we only chose the maximal subgroups P1 the Sylow subgroup P that satisfying .In this paper，we used c -normal properties these P1 to obtain sufficient conditions for p -nilpotent and p -supersolvable groups.To some extent，the obtained results promotes Theorem 3.1，Theorem 3.4，and Theorem 3.8 literature[14].

Keywords： c -normal subgroup; p -nilpotent group ; p -supersolvable group;Sylow subgroup;maximal subgroup

子群的性质对群本身的结构有着重要的影响，其相关课题是有限群论的研究热点之一，并已取得了丰富的研究结果[1-12]。（剩余8374字）