A Kurosh subgroup theorem for free pro-$\mathcal{C}$-products of pro-$\mathcal{C}$-groups

Abstract

Let C be a class of finite groups, closed under finite products, subgroups and homomorphic images. In this paper we define and study free pro-e- products of pro-e- groups indexed by a pointed topological space. Our main result is a structure theorem for open subgroups of such free products along the lines of the Kurosh subgroup theorem for abstract groups. As a consequence we obtain