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arXiv · 2206.02682

The nonabelian product modulo sum

Samuel M. Corson
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Abstract

It is shown that if $\{H_n\}_{n \in ω}$ is a sequence of groups without involutions, with $1 < |H_n| \leq 2^{\aleph_0}$, 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 $\{A_n\}_{n \in ω}$ is a sequence of countably infinite torsion-free abelian groups, then the isomorphism class of the product modulo sum $\prod_{n \in ω} A_n/\bigoplus_{n \in ω} A_n$ is dependent on the sequence.

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Samuel M. Corson. 2023-09-28. The nonabelian product modulo sum. https://doi.org/10.1017/s0013091525000033

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