{"title":"从BURNSIDE环到逆极限的同态核II: G = Cpm × Cpn","authors":"M. Morimoto, Masafumi Sugimura","doi":"10.2206/KYUSHUJM.72.95","DOIUrl":null,"url":null,"abstract":"Let G be a finite group and A(G) the Burnside ring of G. The family of rings A(H), where H ranges over the set of all proper subgroups of G, yields the inverse limit L(G) and a canonical homomorphism from A(G) to L(G) which is called the restriction map. Let Q(G) be the cokernel of this homomorphism. It is known that Q(G) is a finite abelian group and is isomorphic to the cartesian product of Q(G/N (p)), where p runs over the set of primes dividing the order of G and N (p) stands for the smallest normal subgroup of G such that the order of G/N (p) is a power of p. Therefore, it is important to investigate Q(G) for G of prime power order. In this paper we develop a way to compute Q(G) for cartesian products G of two cyclic p-groups.","PeriodicalId":49929,"journal":{"name":"Kyushu Journal of Mathematics","volume":"72 1","pages":"95-105"},"PeriodicalIF":0.6000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"COKERNELS OF HOMOMORPHISMS FROM BURNSIDE RINGS TO INVERSE LIMITS II: G = Cpm × Cpn\",\"authors\":\"M. Morimoto, Masafumi Sugimura\",\"doi\":\"10.2206/KYUSHUJM.72.95\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let G be a finite group and A(G) the Burnside ring of G. The family of rings A(H), where H ranges over the set of all proper subgroups of G, yields the inverse limit L(G) and a canonical homomorphism from A(G) to L(G) which is called the restriction map. Let Q(G) be the cokernel of this homomorphism. It is known that Q(G) is a finite abelian group and is isomorphic to the cartesian product of Q(G/N (p)), where p runs over the set of primes dividing the order of G and N (p) stands for the smallest normal subgroup of G such that the order of G/N (p) is a power of p. Therefore, it is important to investigate Q(G) for G of prime power order. In this paper we develop a way to compute Q(G) for cartesian products G of two cyclic p-groups.\",\"PeriodicalId\":49929,\"journal\":{\"name\":\"Kyushu Journal of Mathematics\",\"volume\":\"72 1\",\"pages\":\"95-105\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kyushu Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2206/KYUSHUJM.72.95\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyushu Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2206/KYUSHUJM.72.95","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
COKERNELS OF HOMOMORPHISMS FROM BURNSIDE RINGS TO INVERSE LIMITS II: G = Cpm × Cpn
Let G be a finite group and A(G) the Burnside ring of G. The family of rings A(H), where H ranges over the set of all proper subgroups of G, yields the inverse limit L(G) and a canonical homomorphism from A(G) to L(G) which is called the restriction map. Let Q(G) be the cokernel of this homomorphism. It is known that Q(G) is a finite abelian group and is isomorphic to the cartesian product of Q(G/N (p)), where p runs over the set of primes dividing the order of G and N (p) stands for the smallest normal subgroup of G such that the order of G/N (p) is a power of p. Therefore, it is important to investigate Q(G) for G of prime power order. In this paper we develop a way to compute Q(G) for cartesian products G of two cyclic p-groups.
期刊介绍:
The Kyushu Journal of Mathematics is an academic journal in mathematics, published by the Faculty of Mathematics at Kyushu University since 1941. It publishes selected research papers in pure and applied mathematics. One volume, published each year, consists of two issues, approximately 20 articles and 400 pages in total.
More than 500 copies of the journal are distributed through exchange contracts between mathematical journals, and available at many universities, institutes and libraries around the world. The on-line version of the journal is published at "Jstage" (an aggregator for e-journals), where all the articles published by the journal since 1995 are accessible freely through the Internet.