{"title":"On ℳ-supplemented subgroups","authors":"Yuedi Zeng","doi":"10.1515/jgth-2021-0195","DOIUrl":null,"url":null,"abstract":"Abstract Let 𝐺 be a finite group and p k p^{k} a prime power dividing | G | \\lvert G\\rvert . A subgroup 𝐻 of 𝐺 is said to be ℳ-supplemented in 𝐺 if there exists a subgroup 𝐾 of 𝐺 such that G = H K G=HK and H i K < G H_{i}K<G for every maximal subgroup H i H_{i} of 𝐻. In this paper, we complete the classification of the finite groups 𝐺 in which all subgroups of order p k p^{k} are ℳ-supplemented. In particular, we show that if k ≥ 2 k\\geq 2 , then G / O p ′ ( G ) G/\\mathbf{O}_{p^{\\prime}}(G) is supersolvable with a normal Sylow 𝑝-subgroup and a cyclic 𝑝-complement.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2021-0195","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract Let 𝐺 be a finite group and p k p^{k} a prime power dividing | G | \lvert G\rvert . A subgroup 𝐻 of 𝐺 is said to be ℳ-supplemented in 𝐺 if there exists a subgroup 𝐾 of 𝐺 such that G = H K G=HK and H i K < G H_{i}K
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