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arXiv · 2608.22913

Uniform exponent bounds for integral group homology

Primoz Moravec
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Abstract

We prove that, in each fixed degree, the exponent of the integral homology of a finite group is bounded solely in terms of the degree and the exponent of the group. The proof combines the solution of the restricted Burnside problem with a representability property of the bar construction and may be viewed as a torsion analogue of the method of acyclic models. We also use the Lyndon--Hochschild--Serre spectral sequence to obtain explicit bounds for finite solvable and nilpotent groups in terms of their derived length and nilpotency class.

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Primoz Moravec. 2026-08-24. Uniform exponent bounds for integral group homology. https://arxiv.org/abs/2608.22913

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