{"title":"群的自由阿贝尔化扩展的同调性","authors":"L. Kovach, Yu. V. Kuz’min, R. Shter","doi":"10.1070/SM1992V072N02ABEH001416","DOIUrl":null,"url":null,"abstract":"Let G be a group given by a free presentation G = F/N, and N' the commutator subgroup of N. The quotient F/N' is called a free abelianized extension of G. We study the homology of F/N' with trivial coefficients. In particular, for torsion-free G our main result yields a complete description of the odd torsion in the integral homology of F/N' in terms of the mod p homology of G.","PeriodicalId":208776,"journal":{"name":"Mathematics of The Ussr-sbornik","volume":"69 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1992-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"HOMOLOGY OF FREE ABELIANIZED EXTENSIONS OF GROUPS\",\"authors\":\"L. Kovach, Yu. V. Kuz’min, R. Shter\",\"doi\":\"10.1070/SM1992V072N02ABEH001416\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a group given by a free presentation G = F/N, and N' the commutator subgroup of N. The quotient F/N' is called a free abelianized extension of G. We study the homology of F/N' with trivial coefficients. In particular, for torsion-free G our main result yields a complete description of the odd torsion in the integral homology of F/N' in terms of the mod p homology of G.\",\"PeriodicalId\":208776,\"journal\":{\"name\":\"Mathematics of The Ussr-sbornik\",\"volume\":\"69 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1992-02-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-sbornik\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/SM1992V072N02ABEH001416\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-sbornik","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/SM1992V072N02ABEH001416","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Let G be a group given by a free presentation G = F/N, and N' the commutator subgroup of N. The quotient F/N' is called a free abelianized extension of G. We study the homology of F/N' with trivial coefficients. In particular, for torsion-free G our main result yields a complete description of the odd torsion in the integral homology of F/N' in terms of the mod p homology of G.
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