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December 2019 Quiver Representations, Group Characters, and Prime Graphs of Finite Groups
Nobuo IIYORI, Masato SAWABE
Tokyo J. Math. 42(2): 497-523 (December 2019). DOI: 10.3836/tjm/1502179297

Abstract

We develop a general theory of quiver representations $\mathcal{F}$ which is motivated by investigating group representations in different characteristics simultaneously. A feature of $\mathcal{F}$ is to assign to each vertex $a$ of the quiver a finite set $\mathcal{F}_{a}$. This result provides a uniform explanation of many objects in group character theory. Furthermore, we give a characterization of when the prime graph $\Gamma(G)$ of a finite group $G$ is disconnected by using group characters. And then, this result on $\Gamma(G)$ can be rephrased in terms of certain quiver representations.

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Nobuo IIYORI. Masato SAWABE. "Quiver Representations, Group Characters, and Prime Graphs of Finite Groups." Tokyo J. Math. 42 (2) 497 - 523, December 2019. https://doi.org/10.3836/tjm/1502179297

Information

Published: December 2019
First available in Project Euclid: 24 August 2019

zbMATH: 07209631
MathSciNet: MR4106590
Digital Object Identifier: 10.3836/tjm/1502179297

Subjects:
Primary: 16G20
Secondary: 20C15

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

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Vol.42 • No. 2 • December 2019
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