The nonabelian product modulo sum

Abstract

It is shown that if {Hn}n∈ω is a sequence of groups without involutions, with 1 < |Hn| ≤ 2 ℵ 0 , then the topologist's product modulo the finite words is (up to isomorphism) independent of the choice of sequence. This contrasts with the abelian setting: if {An}n∈ω is a sequence of countably infinite torsion-free abelian groups, then the isomorphism class of the product modulo sum n∈ω An/ n∈ω An is dependent on the sequence.