Tokyo Journal of Mathematics

Homology of the Complex of All Non-trivial Nilpotent Subgroups of a Finite Non-solvable Group

Nobuo IIYORI and Masato SAWABE

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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.

Article information

Source
Tokyo J. Math., Volume 42, Number 1 (2019), 113-120.

Dates
First available in Project Euclid: 18 July 2019

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1563436916

Mathematical Reviews number (MathSciNet)
MR3982052

Zentralblatt MATH identifier
07114903

Subjects
Primary: 20E15: Chains and lattices of subgroups, subnormal subgroups [See also 20F22]
Secondary: 20D15: Nilpotent groups, $p$-groups

Citation

IIYORI, Nobuo; SAWABE, Masato. Homology of the Complex of All Non-trivial Nilpotent Subgroups of a Finite Non-solvable Group. Tokyo J. Math. 42 (2019), no. 1, 113--120. https://projecteuclid.org/euclid.tjm/1563436916


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