Countable compactness and finite powers of topological groups without convergent sequences

We show under MAcountable that for every positive integer n there exists a topological group G without non-trivial convergent sequences such that Gn is countably compact but Gn+1 is not. This answers the finite case of Comfortʹs Question 477 in the Open Problems in Topology. We also show under MAcountable+2<c=c that there are 2c non-homeomorphic group topologies as above if n⩾2. We apply the construction on suitable sets, answering the finite case of a question of D. Dikranjan on the productivity of suitability and in a topological game defined by Bouziad.