The nonabelian product modulo sum

Abstract

It is shown that if $\{H_n{\}}_{n\in \omega }$ is a sequence of groups without involutions, with $1<|H_n|\le 2^{{\aleph }_0}$, 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 $\{A_n{\}}_{n\in \omega }$ is a sequence of countably infinite torsion-free abelian groups, then the isomorphism class of the product modulo sum ${\prod }_{n\in \omega }{A}_n/{⨁}_{n\in \omega }{A}_n$ is dependent on the sequence.

References in corpus (1)

• The Griffiths double cone group is isomorphic to the triple