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arXiv · 1612.04302

The homotopy types of the posets of p-subgroups of a finite group

Elias Gabriel Minian·Kevin Ivan Piterman
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Abstract

We study the homotopy properties of the posets of p-subgroups Sp(G) and Ap(G) of a finite group G, viewed as finite topological spaces. We answer a question raised by R.E. Stong in 1984 about the relationship between the contractibility of the finite space Ap(G) and that of Sp(G) negatively, and describe the contractibility of Ap(G) in terms of algebraic properties of the group G.

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Elias Gabriel Minian, Kevin Ivan Piterman. 2016-12-13. The homotopy types of the posets of p-subgroups of a finite group. https://arxiv.org/abs/1612.04302

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