{"title":"On $\\mathcal{M}$-normal embedded subgroups and the structure of finite groups","authors":"Ruifang Chen, Xianhe Zhao, Rui Li","doi":"10.7146/math.scand.a-126034","DOIUrl":null,"url":null,"abstract":"Let $G$ be a group and $H$ be a subgroup of $G$. $H$ is said to be $\\mathcal{M}$-normal supplemented in $G$ if there exists a normal subgroup $K$ of $G$ such that $G=HK$ and $H_1K<G$ for every maximal subgroup $H_1$ of $H$. Furthermore, $H$ is said to be $\\mathcal{M}$-normal embedded in $G$ if there exists a normal subgroup $K$ of $G$ such that $G=HK$ and $H\\cap K=1$ or $H\\cap K$ is $\\mathcal{M}$-normal supplemented in $G$. In this paper, some new criteria for a group to be nilpotent and $p$-supersolvable for some prime $p$ are obtained.","PeriodicalId":49873,"journal":{"name":"Mathematica Scandinavica","volume":" ","pages":""},"PeriodicalIF":0.3000,"publicationDate":"2021-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Scandinavica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.7146/math.scand.a-126034","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let $G$ be a group and $H$ be a subgroup of $G$. $H$ is said to be $\mathcal{M}$-normal supplemented in $G$ if there exists a normal subgroup $K$ of $G$ such that $G=HK$ and $H_1K
期刊介绍：
Mathematica Scandinavica is a peer-reviewed journal in mathematics that has been published regularly since 1953. Mathematica Scandinavica is run on a non-profit basis by the five mathematical societies in Scandinavia. It is the aim of the journal to publish high quality mathematical articles of moderate length.
Mathematica Scandinavica publishes about 640 pages per year. For 2020, these will be published as one volume consisting of 3 issues (of 160, 240 and 240 pages, respectively), enabling a slight increase in article pages compared to previous years. The journal aims to publish the first issue by the end of March. Subsequent issues will follow at intervals of approximately 4 months.
All back volumes are available in paper and online from 1953. There is free access to online articles more than five years old.
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