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

Fingerprint

Burnside Ring
Inverse Limit
Homomorphism
Finite Group
Subgroup
Restriction
Conjugation
Morphisms
Denote
Ring
Closed
Family
Object

Keywords

  • Burnside ring
  • Inverse limit
  • Restriction homomorphism

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

The inverse limit of the Burnside ring for a family of subgroups of a finite group. / Hara, Yasuhiro; Morimoto, Masaharu.

In: Hokkaido Mathematical Journal, Vol. 47, No. 2, 01.01.2018, p. 427-444.

Research output: Contribution to journalArticle

@article{e438668a8d2342c8ac31ce6a82f832f5,
title = "The inverse limit of the Burnside ring for a family of subgroups of a finite group",
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.",
keywords = "Burnside ring, Inverse limit, Restriction homomorphism",
author = "Yasuhiro Hara and Masaharu Morimoto",
year = "2018",
month = "1",
day = "1",
language = "English",
volume = "47",
pages = "427--444",
journal = "Hokkaido Mathematical Journal",
issn = "0385-4035",
publisher = "Department of Mathematics, Hokkaido University",
number = "2",

}

TY - JOUR

T1 - The inverse limit of the Burnside ring for a family of subgroups of a finite group

AU - Hara, Yasuhiro

AU - Morimoto, Masaharu

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Burnside ring

KW - Inverse limit

KW - Restriction homomorphism

UR - http://www.scopus.com/inward/record.url?scp=85048679463&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85048679463&partnerID=8YFLogxK

M3 - Article

VL - 47

SP - 427

EP - 444

JO - Hokkaido Mathematical Journal

JF - Hokkaido Mathematical Journal

SN - 0385-4035

IS - 2

ER -