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June 2005 On the Reduced Lefschetz Module and the Centric $p$-Radical Subgroups
Masato SAWABE
Tokyo J. Math. 28(1): 79-90 (June 2005). DOI: 10.3836/tjm/1244208281

Abstract

The purpose of this paper is to show that the reduced Lefschetz module of the $G$-poset $\mathcal{B}_{p}^{cen}(G)$ consisting of all centric $p$-radical subgroups of a finite group $G$ is an $\mathcal{X}$-projective virtual $\mathbb{Z}_{p}[G]$-module where $\mathcal{X}$ is a family of $p$-subgroups of the normalizers of non-centric $p$-radical subgroups of $G$. As corollary, we have a lower bound of the $p$-power of the reduced Euler characteristic $\tilde{\chi}(\mathcal{B}_{p}^{cen}(G))$.

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Masato SAWABE. "On the Reduced Lefschetz Module and the Centric $p$-Radical Subgroups." Tokyo J. Math. 28 (1) 79 - 90, June 2005. https://doi.org/10.3836/tjm/1244208281

Information

Published: June 2005
First available in Project Euclid: 5 June 2009

zbMATH: 1108.20051
MathSciNet: MR2149625
Digital Object Identifier: 10.3836/tjm/1244208281

Rights: Copyright © 2005 Publication Committee for the Tokyo Journal of Mathematics

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Vol.28 • No. 1 • June 2005
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