Uniform exponent bounds for integral group homology

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.