{"title":"具有循环Frattini子群的有限p群的自同构","authors":"R. Soleimani","doi":"10.22108/IJGT.2017.21219","DOIUrl":null,"url":null,"abstract":"Let $G$ be a group and $Aut^{Phi}(G)$ denote the group of all automorphisms of $G$ centralizing $G/Phi(G)$ elementwise. In this paper, we characterize the finite $p$-groups $G$ with cyclic Frattini subgroup for which $|Aut^{Phi}(G):Inn(G)|=p$.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2017-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Automorphisms of a finite $p$-group with cyclic Frattini subgroup\",\"authors\":\"R. Soleimani\",\"doi\":\"10.22108/IJGT.2017.21219\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $G$ be a group and $Aut^{Phi}(G)$ denote the group of all automorphisms of $G$ centralizing $G/Phi(G)$ elementwise. In this paper, we characterize the finite $p$-groups $G$ with cyclic Frattini subgroup for which $|Aut^{Phi}(G):Inn(G)|=p$.\",\"PeriodicalId\":43007,\"journal\":{\"name\":\"International Journal of Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2017-01-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/IJGT.2017.21219\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/IJGT.2017.21219","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Automorphisms of a finite $p$-group with cyclic Frattini subgroup
Let $G$ be a group and $Aut^{Phi}(G)$ denote the group of all automorphisms of $G$ centralizing $G/Phi(G)$ elementwise. In this paper, we characterize the finite $p$-groups $G$ with cyclic Frattini subgroup for which $|Aut^{Phi}(G):Inn(G)|=p$.
期刊介绍：
International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.
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