{"title":"循环嵌入的有限直接和","authors":"J. Kosakowska, M. Schmidmeier","doi":"10.1090/CONM/761/15314","DOIUrl":null,"url":null,"abstract":"In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group given in his 1951 book ``Infinite Abelian Groups''. For this we introduce partial maps on Littlewood-Richardson tableaux and show that they characterize the isomorphism types of finite direct sums of such cyclic embeddings.","PeriodicalId":325430,"journal":{"name":"Advances in Representation Theory of\n Algebras","volume":"20 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2019-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Finite direct sums of cyclic\\n embeddings\",\"authors\":\"J. Kosakowska, M. Schmidmeier\",\"doi\":\"10.1090/CONM/761/15314\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group given in his 1951 book ``Infinite Abelian Groups''. For this we introduce partial maps on Littlewood-Richardson tableaux and show that they characterize the isomorphism types of finite direct sums of such cyclic embeddings.\",\"PeriodicalId\":325430,\"journal\":{\"name\":\"Advances in Representation Theory of\\n Algebras\",\"volume\":\"20 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-05-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Representation Theory of\\n Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/CONM/761/15314\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Representation Theory of\n Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/CONM/761/15314","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper we generalize Kaplansky's combinatorial characterization of the isomorphism types of embeddings of a cyclic subgroup in a finite abelian group given in his 1951 book ``Infinite Abelian Groups''. For this we introduce partial maps on Littlewood-Richardson tableaux and show that they characterize the isomorphism types of finite direct sums of such cyclic embeddings.
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