{"title":"关于所有最小子群都是 BNA 子群的有限群","authors":"Yanhui Wang, Xiuyun Guo","doi":"10.4171/rsmup/157","DOIUrl":null,"url":null,"abstract":"– A subgroup 𝐻 of a group 𝐺 is said to be a 𝐵𝑁𝐴 -subgroup of 𝐺 if either 𝐻 𝑥 = 𝐻 or 𝑥 ∈ ⟨ 𝐻, 𝐻 𝑥 ⟩ for all 𝑥 ∈ 𝐺 . The purpose of this paper is first to give the best bound for the Fitting height of 𝐺 if all minimal subgroups of 𝐺 are 𝐵𝑁𝐴 -subgroups of 𝐺 , and next give an answer for the question of the paper [On 𝐵𝑁𝐴 -normality and solvability of finite groups, Rend. Sem. Mat. Univ. Padova 136 (2016), 51-60]. Finally we use few 𝐵𝑁𝐴 -subgroups of prime order to determine the structure of the finite groups. In fact, some new conditions for a finite group to be supersolvable have been given.","PeriodicalId":20997,"journal":{"name":"Rendiconti del Seminario Matematico della Università di Padova","volume":"97 8","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On finite groups in which all minimal subgroups are BNA-subgroups\",\"authors\":\"Yanhui Wang, Xiuyun Guo\",\"doi\":\"10.4171/rsmup/157\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"– A subgroup 𝐻 of a group 𝐺 is said to be a 𝐵𝑁𝐴 -subgroup of 𝐺 if either 𝐻 𝑥 = 𝐻 or 𝑥 ∈ ⟨ 𝐻, 𝐻 𝑥 ⟩ for all 𝑥 ∈ 𝐺 . The purpose of this paper is first to give the best bound for the Fitting height of 𝐺 if all minimal subgroups of 𝐺 are 𝐵𝑁𝐴 -subgroups of 𝐺 , and next give an answer for the question of the paper [On 𝐵𝑁𝐴 -normality and solvability of finite groups, Rend. Sem. Mat. Univ. Padova 136 (2016), 51-60]. Finally we use few 𝐵𝑁𝐴 -subgroups of prime order to determine the structure of the finite groups. In fact, some new conditions for a finite group to be supersolvable have been given.\",\"PeriodicalId\":20997,\"journal\":{\"name\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"volume\":\"97 8\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-03-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Seminario Matematico della Università di Padova\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/rsmup/157\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Seminario Matematico della Università di Padova","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/rsmup/157","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On finite groups in which all minimal subgroups are BNA-subgroups
– A subgroup 𝐻 of a group 𝐺 is said to be a 𝐵𝑁𝐴 -subgroup of 𝐺 if either 𝐻 𝑥 = 𝐻 or 𝑥 ∈ ⟨ 𝐻, 𝐻 𝑥 ⟩ for all 𝑥 ∈ 𝐺 . The purpose of this paper is first to give the best bound for the Fitting height of 𝐺 if all minimal subgroups of 𝐺 are 𝐵𝑁𝐴 -subgroups of 𝐺 , and next give an answer for the question of the paper [On 𝐵𝑁𝐴 -normality and solvability of finite groups, Rend. Sem. Mat. Univ. Padova 136 (2016), 51-60]. Finally we use few 𝐵𝑁𝐴 -subgroups of prime order to determine the structure of the finite groups. In fact, some new conditions for a finite group to be supersolvable have been given.
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