### 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 res_{F}
^{G}: A(G) → A(F). We study this restriction homomorphism.

Original language | English |
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Pages (from-to) | 427-444 |

Number of pages | 18 |

Journal | Hokkaido Mathematical Journal |

Volume | 47 |

Issue number | 2 |

Publication status | Published - Jan 1 2018 |

### Fingerprint

### Keywords

- Burnside ring
- Inverse limit
- Restriction homomorphism

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Hokkaido Mathematical Journal*,

*47*(2), 427-444.

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

Research output: Contribution to journal › Article

*Hokkaido Mathematical Journal*, vol. 47, no. 2, pp. 427-444.

}

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

AN - SCOPUS:85048679463

VL - 47

SP - 427

EP - 444

JO - Hokkaido Mathematical Journal

JF - Hokkaido Mathematical Journal

SN - 0385-4035

IS - 2

ER -