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Finite Groups with p-Supersolvable normalizers of p-Subgroups

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Journal of Mathematical Research with Applications 2022年第5期42卷 476-480页

作者： Tingting QIU Jinlian WU Jia ZHANG School of Mathematics and Information China West Normal University Yancheng Biological Engineering Higher Vocational Technology School

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 ≤ p~d<|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?K and P′≤ K≤ 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

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Finite NPDM-groups

Acta Mathematica Sinica,English Series 2021年第2期37卷 306-314页

作者： Jian Ji CAO Xiu Yun GUO School of Applied Mathematics Shanxi University of Finance and EconomicsTaiyuan 030006P.R.China Department of Mathematics Shanghai UniversityShanghai 200444P.R.China

In this paper the classification is given for finite groups in which the normalizer of every non-normal cyclic subgroup of order divided by the minimal prime of |G| is a maximal subgroup.

关键词： normalizer cyclic subgroup maximal subgroup

On the group with the same orders of Sylow nor-malizers as the finite projective special unitary group

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Science China Mathematics 2004年第6期47卷 801-811页

作者： Bl JianxingDepartment of Mathematics, Liaoning University, Shenyang 110036, China Department of Mathematics Liaoning University Shenyang China

In this paper we prove that a finite group G is isomorphic to the finite projective special unitary group U n (q) if and only if they have the same order of Sylow r-normalizer for every prime r.

关键词：单一的组 Sylow 亚群 normalizer

The Structure of One Type of Non-Abelian Group

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Wuhan University Journal of Natural Sciences 2002年第1期7卷 6-8页

作者： Huang Ben-wen Yu Chu-xiong School of Mathematics and Statistics Wuhan University Wuhan Hubei China

By the property of the solvable group and the extending theorem of group, the authors acquired the structure of one type of Non-Abelian group. And we proved that when order is 10p n (p#2,5) and the sylowp-subgroup is ... 详细信息

关键词： solvable group fitting subgroup centralizer normalizer

A Characterization of L_n(q) by the normalizers' Orders of Their Sylow Subgroups

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Acta Mathematica Sinica,English Series 1995年第3期11卷 300-306页

作者： Bi Jianxing Department of Mathematics Liaoning University Shenyang

Let G be a finite group. If |NG（R1）|=|NLn（q）（R2）| for every prime r, where R1∈Sylr G and R2∈Sylr（Ln（q））, then G≌Ln（q）.

关键词： Finite simple group Sylow subgroup normalizer

Structure of Groups with Generalized Normal Subgroups

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Advances in Pure Mathematics 2014年第6期4卷 261-268页

作者： Mohammad Arshaduzzaman Department of Mathematics College of Science Al Baha University Al Baha KSA

The present paper deals with a subgroup X of a group G is almost normal if the index |G: NG(X)| is finite, while X is nearly normal if it has finite index in the normal closure XG. This paper investigates the structur... 详细信息

关键词： Normality Nearly Normality normalizer Subgroup

Two Theorems about Nilpotent Subgroup

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Applied Mathematics 2011年第5期2卷 562-564页

作者： Lijiang Zeng 不详

In the paper, we introduce some concepts and notations of Hall π-subgroup etc, and prove some properties about finite p-group, nilpotent group and Sylow p-subgroup. Finally, we have proved two interesting theorems ab... 详细信息

关键词： Hall π-Subgroup Sylow p-Subgroup normalizer Nilpotent Group