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June 2018 The inverse limit of the Burnside ring for a family of subgroups of a finite group
Yasuhiro HARA, Masaharu MORIMOTO
Hokkaido Math. J. 47(2): 427-444 (June 2018). DOI: 10.14492/hokmj/1529308826

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.

Citation

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Yasuhiro HARA. Masaharu MORIMOTO. "The inverse limit of the Burnside ring for a family of subgroups of a finite group." Hokkaido Math. J. 47 (2) 427 - 444, June 2018. https://doi.org/10.14492/hokmj/1529308826

Information

Published: June 2018
First available in Project Euclid: 18 June 2018

zbMATH: 06901713
MathSciNet: MR3815300
Digital Object Identifier: 10.14492/hokmj/1529308826

Subjects:
Primary: 19A22
Secondary: 57S17

Rights: Copyright © 2018 Hokkaido University, Department of Mathematics

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Vol.47 • No. 2 • June 2018
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