Tokyo Journal of Mathematics

On the Reduced Lefschetz Module and the Centric $p$-Radical Subgroups

Masato SAWABE

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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 $\tilde{\chi}(\mathcal{B}_{p}^{cen}(G))$.

Article information

Source
Tokyo J. Math., Volume 28, Number 1 (2005), 79-90.

Dates
First available in Project Euclid: 5 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1244208281

Digital Object Identifier
doi:10.3836/tjm/1244208281

Mathematical Reviews number (MathSciNet)
MR2149625

Zentralblatt MATH identifier
1108.20051

Citation

SAWABE, Masato. On the Reduced Lefschetz Module and the Centric $p$-Radical Subgroups. Tokyo J. Math. 28 (2005), no. 1, 79--90. doi:10.3836/tjm/1244208281. https://projecteuclid.org/euclid.tjm/1244208281


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