The inverse limit of the Burnside ring for a family of subgroups of a finite group

Yasuhiro Hara, Masaharu Morimoto

Research output: Contribution to journalArticle

Abstract

Let G be a finite nontrivial group and A(G) the Burnside ring of G. Let F be a set of subgroups of G which is closed under taking subgroups and taking conjugations by elements in G. Then let F denote the category whose objects are elements in F and whose morphisms are triples (H; g;K) such that H, K ∈ F and g ∈ G with gHg-1 ⊂ K. Taking the inverse limit of A(H), where H ∈ F, we obtain the ring A(F) and the restriction homomorphism resF G: A(G) → A(F). We study this restriction homomorphism.

Original languageEnglish
Pages (from-to)427-444
Number of pages18
JournalHokkaido Mathematical Journal
Volume47
Issue number2
Publication statusPublished - Jan 1 2018

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Keywords

  • Burnside ring
  • Inverse limit
  • Restriction homomorphism

ASJC Scopus subject areas

  • Mathematics(all)

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