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June 2019 Homology of the Complex of All Non-trivial Nilpotent Subgroups of a Finite Non-solvable Group
Nobuo IIYORI, Masato SAWABE
Tokyo J. Math. 42(1): 113-120 (June 2019). DOI: 10.3836/tjm/1502179264

Abstract

Let $G$ be a finite non-solvable group. We study homology of the complex $\mathcal{N}(G)$ of all non-trivial nilpotent subgroups of $G$. The determination of $H_{n}(\mathcal{N}(G))$ is reduced to that of homology of its subcomplex $\mathcal{N}_{\pi_{1}}(G)$ consisting of all nilpotent $\pi_{1}$-subgroups, where $\pi_{1}$ is the connected component of the prime graph of $G$ containing 2. Furthermore, $\mathcal{N}_{\pi_{1}}(G)$ is connected if $G$ possesses no strongly embedded subgroups.

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Nobuo IIYORI. Masato SAWABE. "Homology of the Complex of All Non-trivial Nilpotent Subgroups of a Finite Non-solvable Group." Tokyo J. Math. 42 (1) 113 - 120, June 2019. https://doi.org/10.3836/tjm/1502179264

Information

Published: June 2019
First available in Project Euclid: 18 July 2019

zbMATH: 07114903
MathSciNet: MR3982052
Digital Object Identifier: 10.3836/tjm/1502179264

Subjects:
Primary: 20E15
Secondary: 20D15

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

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Vol.42 • No. 1 • June 2019
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