Finite Groups with p-Supersolvable Normalizers of p-Subgroups  

作　　者：Tingting QIU Jinlian WU Jia ZHANG 

机构地区：[1]Yancheng Biological Engineering Higher Vocational Technology School,Jiangsu 224051,P.R.China [2]School of Mathematics and Information,China West Normal University,Sichuan637009,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2022年第5期476-480,共5页数学研究及应用（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12001436);the Natural Science Foundation of Sichuan Province(Grant No.2022NSFSC1843);Chunhui Plan Cooperative Scientific Research Project of Ministry of Education of the People’s Republic of China;the Fundamental Research Funds of China West Normal University(Grant Nos.17E091;18B032);。

摘　　要：In the literature, p-nilpotency of the normalizers of p-subgroups has an important influence on finite p-nilpotent groups. In this paper, we extend the p-nilpotency to psupersolvability and choose every normal p-subgroups H of P such that |H| = pdand explore p-supersolvability of G by the conditions of weakly M-supplemented properties of H and psupersolvability of the normalizer NG(H), where 1 ≤ pd<|P |. Also, we study the p-nilpotency of G under the assumptions that NG(P) is p-nilpotent and the weakly M-supplemented condition on a subgroup K such that K_(p)■K and P′≤ K_(p) ≤ Φ(P), Kp is a Sylow p-subgroup K. To some extent, our main results can be regarded as generalizations of the Frobenius theorem.

关 键 词：NORMALIZER weakly M-supplemented subgroup p-supersolvability p-nilpotency 

分 类 号：O152.1[理学—数学]