Cokernels of homomorphisms from burnside rings to inverse limits II: G = Cpm × Cpn

Masaharu Morimoto, Masafumi Sugimura

Research output: Contribution to journalArticle

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.

Original languageEnglish
Pages (from-to)95-105
Number of pages11
JournalKyushu Journal of Mathematics
Volume72
Issue number1
DOIs
Publication statusPublished - Jan 1 2018

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Keywords

  • Burnside ring
  • Finite group
  • Inverse limit

ASJC Scopus subject areas

  • Mathematics(all)

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