Relative homology of invariant group chains

Let Q be a finite group acting by automorphisms on a discrete group G. K. Knudson has introduced the homology of invariant group chains H*Q (G, A). A useful tool in homology is its relative version. In this paper we introduce the homology of Q- permutation representations as a generalization of the homology of permutation representations defined by Snapper. We prove the existence of a spectral sequence which converges to the homology of a Q-permutation representation. We also introduce a relative version of the homology of invariant group chains using the notion of Q-permutation representations following Adamson and give a topological interpretation of that relative homology. (c) 2023 Elsevier B.V. All rights reserved.