COKERNELS OF HOMOMORPHISMS FROM BURNSIDE RINGS TO INVERSE LIMITS II: G = Cpm × Cpn

IF 0.6 4区 数学 Q3 MATHEMATICS
M. Morimoto, Masafumi Sugimura
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引用次数: 0

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.
从BURNSIDE环到逆极限的同态核II: G = Cpm × Cpn
设G是一个有限群,a (G)是G的Burnside环。环族a (H),其中H作用于G的所有固有子群的集合上,得到了逆极限L(G)和从a (G)到L(G)的正则同态,称为限制映射。设Q(G)是这个同态的核。已知Q(G)是一个有限阿贝尔群,与Q(G/N (p))的笛卡尔积同构,其中p遍历除以G阶的素数集合,N (p)表示G的最小正规子群,使得G/N (p)的阶是p的幂次。因此,研究Q(G)对于素数幂次的G是很重要的。本文给出了计算两个循环p群的笛卡尔积G的Q(G)的一种方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.80
自引率
0.00%
发文量
10
审稿时长
>12 weeks
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.
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