{"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}
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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 $C_{n} \ , \ C_{2}$.
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