{"title":"半直积群的编码矩阵","authors":"Amnah Alkinani, Ahmed A. Khammash","doi":"10.33401/fujma.690424","DOIUrl":null,"url":null,"abstract":"We shall determine the coding matrix of the semi-direct product group $ G = C_{n} \\rtimes_{\\phi} C_{m} $ ; $ \\phi : C_{m} \\longrightarrow Aut(C_{n}) $ of two cyclic groups in order to generalize the known result for the dihedral group $D_{2n}$, which is known to be a semi-direct of the two cyclic groups $C_{n} \\ , \\ C_{2}$.","PeriodicalId":199091,"journal":{"name":"Fundamental Journal of Mathematics and Applications","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Coding Matrices for the Semi-Direct Product Groups\",\"authors\":\"Amnah Alkinani, Ahmed A. Khammash\",\"doi\":\"10.33401/fujma.690424\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We shall determine the coding matrix of the semi-direct product group $ G = C_{n} \\\\rtimes_{\\\\phi} C_{m} $ ; $ \\\\phi : C_{m} \\\\longrightarrow Aut(C_{n}) $ of two cyclic groups in order to generalize the known result for the dihedral group $D_{2n}$, which is known to be a semi-direct of the two cyclic groups $C_{n} \\\\ , \\\\ C_{2}$.\",\"PeriodicalId\":199091,\"journal\":{\"name\":\"Fundamental Journal of Mathematics and Applications\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fundamental Journal of Mathematics and Applications\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33401/fujma.690424\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fundamental Journal of Mathematics and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33401/fujma.690424","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Coding Matrices for the Semi-Direct Product Groups
We shall determine the coding matrix of the semi-direct product group $ G = C_{n} \rtimes_{\phi} C_{m} $ ; $ \phi : C_{m} \longrightarrow Aut(C_{n}) $ of two cyclic groups in order to generalize the known result for the dihedral group $D_{2n}$, which is known to be a semi-direct of the two cyclic groups $C_{n} \ , \ C_{2}$.
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