## Hokkaido Mathematical Journal

- Hokkaido Math. J.
- Volume 47, Number 2 (2018), 427-444.

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

Yasuhiro HARA and Masaharu MORIMOTO

#### Abstract

Let $G$ be a finite nontrivial group and $A(G)$ the Burnside ring of $G$. Let $\mathcal{F}$ be a set of subgroups of $G$ which is closed under taking subgroups and taking conjugations by elements in $G$. Then let $\frak{F}$ denote the category whose objects are elements in $\mathcal{F}$ and whose morphisms are triples $(H, g, K)$ such that $H$, $K \in \mathcal{F}$ and $g \in G$ with $gHg^{-1} \subset K$. Taking the inverse limit of $A(H)$, where $H \in \mathcal{F}$, we obtain the ring $A(\frak{F})$ and the restriction homomorphism ${\rm{res}}^G_{\mathcal{F}} : A(G) \to A(\frak{F})$. We study this restriction homomorphism.

#### Article information

**Source**

Hokkaido Math. J., Volume 47, Number 2 (2018), 427-444.

**Dates**

First available in Project Euclid: 18 June 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.hokmj/1529308826

**Digital Object Identifier**

doi:10.14492/hokmj/1529308826

**Mathematical Reviews number (MathSciNet)**

MR3815300

**Zentralblatt MATH identifier**

06901713

**Subjects**

Primary: 19A22: Frobenius induction, Burnside and representation rings

Secondary: 57S17: Finite transformation groups

**Keywords**

Burnside ring restriction homomorphism inverse limit

#### Citation

HARA, Yasuhiro; MORIMOTO, Masaharu. The inverse limit of the Burnside ring for a family of subgroups of a finite group. Hokkaido Math. J. 47 (2018), no. 2, 427--444. doi:10.14492/hokmj/1529308826. https://projecteuclid.org/euclid.hokmj/1529308826