{"title":"超群公理对群的独立性","authors":"Sh. Navasardyan","doi":"10.52737/18291163-2021.13.12-1-11","DOIUrl":null,"url":null,"abstract":"The independence of the axioms of hypergroup over the group is proven. The proof is composed of two parts. In the first part, the independence of the axioms $(P3), (A1), (A3), (A5)$ in the system of axioms of hypergroup over the group is shown by fixing the structural mappings $\\Phi$ and $\\Xi$. In the same way, in the second part of the proof, the independence of the axioms $(P1), (P2), (A2), (A4)$ is shown by fixing $\\Psi$ and $\\Lambda$.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Independence of the Axioms of Hypergroup over the Group\",\"authors\":\"Sh. Navasardyan\",\"doi\":\"10.52737/18291163-2021.13.12-1-11\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The independence of the axioms of hypergroup over the group is proven. The proof is composed of two parts. In the first part, the independence of the axioms $(P3), (A1), (A3), (A5)$ in the system of axioms of hypergroup over the group is shown by fixing the structural mappings $\\\\Phi$ and $\\\\Xi$. In the same way, in the second part of the proof, the independence of the axioms $(P1), (P2), (A2), (A4)$ is shown by fixing $\\\\Psi$ and $\\\\Lambda$.\",\"PeriodicalId\":42323,\"journal\":{\"name\":\"Armenian Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2021-12-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Armenian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52737/18291163-2021.13.12-1-11\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Armenian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52737/18291163-2021.13.12-1-11","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Independence of the Axioms of Hypergroup over the Group
The independence of the axioms of hypergroup over the group is proven. The proof is composed of two parts. In the first part, the independence of the axioms $(P3), (A1), (A3), (A5)$ in the system of axioms of hypergroup over the group is shown by fixing the structural mappings $\Phi$ and $\Xi$. In the same way, in the second part of the proof, the independence of the axioms $(P1), (P2), (A2), (A4)$ is shown by fixing $\Psi$ and $\Lambda$.
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