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The nonabelian product modulo sum
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society , First View
- Published online by Cambridge University Press:
- 11 April 2025, pp. 1-41
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It is shown that if
$\{H_n\}_{n \in \omega}$ is a sequence of groups without involutions, with 
$1 \lt |H_n| \leq 2^{\aleph_0}$, 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 
$\prod_{n \in \omega} A_n/\bigoplus_{n \in \omega} A_n$ is dependent on the sequence.
