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arXiv · 1401.7513

Truncated Quillen coplexes of p-groups

Francesco Fumagalli·John Shareshian
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Abstract

Let p be an odd prime and let P be a p-group. We examine the order complex of the poset of elementary abelian subgroups of P having order at least p^2. S. Bouc and J. Thévenaz showed that this complex has the homotopy type of a wedge of spheres. We show that, for each nonnegative integer l, the number of spheres of dimension l in this wedge is controlled by the number of extraspecial subgroups X of P having order p^{2l+3} and satisfying Omega_1(C_P(X))=Z(X). We go on to provide a negative answer to a question raised by Bouc and Thévenaz concerning restrictions on the homology groups of the given complex.

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Francesco Fumagalli, John Shareshian. 2014-01-29. Truncated Quillen coplexes of p-groups. https://arxiv.org/abs/1401.7513

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