Equivariant self-homotopy equivalences of product spaces

Abstract

Let G be a finite group. We study the group of G-equivariant self-homotopy equivalences of product of G-spaces. For a product of n number of G-spaces, we represent it as product of n number of subgroups under the assumption of equivariant reducibility. Further we describe each factor as a split short exact sequence. Also we obtain another kind of factorisation, called LU type decomposition, as product of two subgroups.