{"title":"遗传完全序子集","authors":"S. Vinod, S. Sajikumar, G. S. Biju","doi":"10.37193/cmi.2023.01.12","DOIUrl":null,"url":null,"abstract":"A finite group $G$ is said to be a POS-group if, for each $x\\in G$, the cardinality of the set $\\{y\\in G\\,\\,:\\,\\, o(y)=o(x)\\}$ is a divisor of the order of $G$. A POS-group $G$ is said to be a Hereditary Perfect Order Subset group if all even order subgroups of $G$ are POS-group. In this paper we study the structure of Hereditary perfect order subset groups.","PeriodicalId":112946,"journal":{"name":"Creative Mathematics and Informatics","volume":"81 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hereditary Perfect Order Subset Groups\",\"authors\":\"S. Vinod, S. Sajikumar, G. S. Biju\",\"doi\":\"10.37193/cmi.2023.01.12\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A finite group $G$ is said to be a POS-group if, for each $x\\\\in G$, the cardinality of the set $\\\\{y\\\\in G\\\\,\\\\,:\\\\,\\\\, o(y)=o(x)\\\\}$ is a divisor of the order of $G$. A POS-group $G$ is said to be a Hereditary Perfect Order Subset group if all even order subgroups of $G$ are POS-group. In this paper we study the structure of Hereditary perfect order subset groups.\",\"PeriodicalId\":112946,\"journal\":{\"name\":\"Creative Mathematics and Informatics\",\"volume\":\"81 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Creative Mathematics and Informatics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37193/cmi.2023.01.12\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Creative Mathematics and Informatics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37193/cmi.2023.01.12","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A finite group $G$ is said to be a POS-group if, for each $x\in G$, the cardinality of the set $\{y\in G\,\,:\,\, o(y)=o(x)\}$ is a divisor of the order of $G$. A POS-group $G$ is said to be a Hereditary Perfect Order Subset group if all even order subgroups of $G$ are POS-group. In this paper we study the structure of Hereditary perfect order subset groups.
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