Hokkaido Mathematical Journal

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

Yasuhiro HARA and Masaharu MORIMOTO

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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


Export citation