GROUPS WHOSE NONNORMAL SUBGROUPS ARE METAHAMILTONIAN

Author:

ESPOSITO DARIOORCID,DE GIOVANNI FRANCESCOORCID,TROMBETTI MARCOORCID

Abstract

If $\mathfrak{X}$ is a class of groups, we define a sequence $\mathfrak{X}_{1},\mathfrak{X}_{2},\ldots ,\mathfrak{X}_{k},\ldots$ of group classes by putting $\mathfrak{X}_{1}=\mathfrak{X}$ and choosing $\mathfrak{X}_{k+1}$ as the class of all groups whose nonnormal subgroups belong to $\mathfrak{X}_{k}$. In particular, if $\mathfrak{A}$ is the class of abelian groups, $\mathfrak{A}_{2}$ is the class of metahamiltonian groups, that is, groups whose nonnormal subgroups are abelian. The aim of this paper is to study the structure of $\mathfrak{X}_{k}$-groups, with special emphasis on the case $\mathfrak{X}=\mathfrak{A}$. Among other results, it will be proved that a group has a finite commutator subgroup if and only if it is locally graded and belongs to $\mathfrak{A}_{k}$ for some positive integer $k$.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference16 articles.

1. [7] de Giovanni, F. and Trombetti, M. , ‘Cohopfian groups and accessible group classes’, to appear.

2. Groups with restrictions on proper uncountable subgroups;de Giovanni;Studia Sci. Math. Hungar.,2019

3. Überauflösbare Gruppen

4. Structure of solvable nonnilpotent metahamiltonian groups

5. [6] de Giovanni, F. and Trombetti, M. , ‘Groups whose proper subgroups are metahamiltonian-by-finite’, Rocky Mountain J. Math., to appear.

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. A Compendium of Infinite Group Theory: Part 1—Countable Recognizability;Mathematics;2021-09-24

2. Cohopfian groups and accessible group classes;Pacific Journal of Mathematics;2021-08-31

3. GROUPS WITH MANY PRONORMAL SUBGROUPS;Bulletin of the Australian Mathematical Society;2021-05-11

4. A local study of group classes;NOTE MAT;2020

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3