A. A. Basheer, O. V. Shtawzen, Maretta Sarkis, Rozina Ali
{"title":"关于有限非单群的一些结果","authors":"A. A. Basheer, O. V. Shtawzen, Maretta Sarkis, Rozina Ali","doi":"10.54216/gjmsa.010203","DOIUrl":null,"url":null,"abstract":"This paper is dedicated to study some properties of finite groups, where we present the following results: 1) If all centralizers of a group G are cyclic, then G is not simple. 2) If the center of the subgroup A is not trivial and B is cyclic, then G=AB is not simple. On the other hand, we define the m-solvable groups, and we examine some of their elementary properties.","PeriodicalId":299243,"journal":{"name":"Galoitica: Journal of Mathematical Structures and Applications","volume":"36 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Some Results about Finite Non Simple Groups\",\"authors\":\"A. A. Basheer, O. V. Shtawzen, Maretta Sarkis, Rozina Ali\",\"doi\":\"10.54216/gjmsa.010203\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper is dedicated to study some properties of finite groups, where we present the following results: 1) If all centralizers of a group G are cyclic, then G is not simple. 2) If the center of the subgroup A is not trivial and B is cyclic, then G=AB is not simple. On the other hand, we define the m-solvable groups, and we examine some of their elementary properties.\",\"PeriodicalId\":299243,\"journal\":{\"name\":\"Galoitica: Journal of Mathematical Structures and Applications\",\"volume\":\"36 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Galoitica: Journal of Mathematical Structures and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.54216/gjmsa.010203\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Galoitica: Journal of Mathematical Structures and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.54216/gjmsa.010203","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This paper is dedicated to study some properties of finite groups, where we present the following results: 1) If all centralizers of a group G are cyclic, then G is not simple. 2) If the center of the subgroup A is not trivial and B is cyclic, then G=AB is not simple. On the other hand, we define the m-solvable groups, and we examine some of their elementary properties.
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