{"title":"关于补充了tag的子组","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":50188,"journal":{"name":"Journal of Group Theory","volume":"11 1","pages":"1099 - 1107"},"PeriodicalIF":0.4000,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":50188,\"journal\":{\"name\":\"Journal of Group Theory\",\"volume\":\"11 1\",\"pages\":\"1099 - 1107\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-03-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Group Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1515/jgth-2021-0195\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Group Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2021-0195","RegionNum":3,"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
摘要
摘要设𝐺为有限群，p k p^{k}为素数幂除以| G | \lvert G \rvert。如果𝐺存在一个子群𝐾，使得对于𝐻的每一个极大子群H i H＿i, G=H∑K G=HK且H i∑K本文章由计算机程序翻译，如有差异，请以英文原文为准。
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
期刊介绍：
The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.
Topics:
Group Theory-
Representation Theory of Groups-
Computational Aspects of Group Theory-
Combinatorics and Graph Theory-
Algebra and Number Theory
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