Cokernels of Homomorphisms from Burnside Rings to Inverse Limits
Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 165-172
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Let $G$ be a finite group and let $A\left( G \right)$ denote the Burnside ring of $G$ . Then an inverse limit $L\left( G \right)$ of the groups $A\left( H \right)$ for proper subgroups $H$ of $G$ and a homomorphism res from $A\left( G \right)$ to $L\left( G \right)$ are obtained in a natural way. Let $Q\left( G \right)$ denote the cokernel of res. For a prime $p$ , let $N\left( p \right)$ be the minimal normal subgroup of $G$ such that the order of ${G}/{N}\;\left( p \right)$ is a power of $p$ , possibly 1. In this paper we prove that $Q\left( G \right)$ is isomorphic to the cartesian product of the groups $Q\left( {G}/{N\left( p \right)}\; \right)$ , where $p$ ranges over the primes dividing the order of $G$ .
Morimoto, Masaharu. Cokernels of Homomorphisms from Burnside Rings to Inverse Limits. Canadian mathematical bulletin, Tome 60 (2017) no. 1, pp. 165-172. doi: 10.4153/CMB-2016-068-6
@article{10_4153_CMB_2016_068_6,
author = {Morimoto, Masaharu},
title = {Cokernels of {Homomorphisms} from {Burnside} {Rings} to {Inverse} {Limits}},
journal = {Canadian mathematical bulletin},
pages = {165--172},
year = {2017},
volume = {60},
number = {1},
doi = {10.4153/CMB-2016-068-6},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-068-6/}
}
TY - JOUR AU - Morimoto, Masaharu TI - Cokernels of Homomorphisms from Burnside Rings to Inverse Limits JO - Canadian mathematical bulletin PY - 2017 SP - 165 EP - 172 VL - 60 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2016-068-6/ DO - 10.4153/CMB-2016-068-6 ID - 10_4153_CMB_2016_068_6 ER -
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