Cokernels of Homomorphisms from Burnside Rings to Inverse Limits

Canadian mathematical bulletin

Masaharu Morimoto¹ 

[1] Graduate School of Natural Science and Technology, Okayama University, Tsushimanaka 3-1-1, Kitaku, Okayama, 700-8530 Japan

关键词: Burnside ring;    inverse limit;    finite group;   

DOI  :  10.4153/CMB-2016-068-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $G$ be a finite group and let $A(G)$ denote the Burnside ring of $G$. Then an inverse limit $L(G)$ of the groups $A(H)$ for proper subgroups $H$ of $G$ and a homomorphism ${operatorname{res}}$ from $A(G)$ to $L(G)$ are obtained in a naturalway. Let $Q(G)$ denote the cokernel of ${operatorname{res}}$. For a prime $p$, let $N(p)$ be the minimal normal subgroup of $G$ such that the order of $G/N(p)$ is a power of $p$, possibly $1$. In this paper we prove that $Q(G)$ is isomorphic to the cartesian product of the groups $Q(G/N(p))$, where $p$ ranges over the primes dividing the order of $G$.

【 授权许可】

Unknown