TY - JOUR

T1 - Cokernels of homomorphisms from burnside rings to inverse limits

AU - Morimoto, Masaharu

N1 - Publisher Copyright:
© 2016 Canadian Mathematical Society.

PY - 2017/3

Y1 - 2017/3

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.

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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 -