### Abstract

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 res from A(G) to L(G) are obtained in a natural way. Let Q(G) denote the cokernel of 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.

Original language | English |
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Pages (from-to) | 165-172 |

Number of pages | 8 |

Journal | Canadian Mathematical Bulletin |

Volume | 60 |

Issue number | 1 |

DOIs | |

Publication status | Published - Mar 1 2017 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**Cokernels of homomorphisms from burnside rings to inverse limits.** / Morimoto, Masaharu.

Research output: Contribution to journal › Article

*Canadian Mathematical Bulletin*, vol. 60, no. 1, pp. 165-172. https://doi.org/10.4153/CMB-2016-068-6

}

TY - JOUR

T1 - Cokernels of homomorphisms from burnside rings to inverse limits

AU - Morimoto, Masaharu

PY - 2017/3/1

Y1 - 2017/3/1

N2 - 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 res from A(G) to L(G) are obtained in a natural way. Let Q(G) denote the cokernel of 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.

AB - 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 res from A(G) to L(G) are obtained in a natural way. Let Q(G) denote the cokernel of 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.

UR - http://www.scopus.com/inward/record.url?scp=85009383596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009383596&partnerID=8YFLogxK

U2 - 10.4153/CMB-2016-068-6

DO - 10.4153/CMB-2016-068-6

M3 - Article

AN - SCOPUS:85009383596

VL - 60

SP - 165

EP - 172

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

SN - 0008-4395

IS - 1

ER -