The nonabelian product modulo sum

2022/06/06 by Samuel M. Corson, Corson, Samuel M. · 1 citation
Computer Science · Mathematics · #03E75 #20A15 #55Q52 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2206.02682

openalex publication_date 2022/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is shown that if \H_n\_{n ∈ ω} is a sequence of groups without involutions, with 1 < |H_n| ≤ 2^ℵ₀, 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 ∈ ω} is a sequence of countably infinite torsion-free abelian groups, then the isomorphism class of the product modulo sum ∏_{n ∈ ω} A_n/\bigoplus_{n ∈ ω} A_n is dependent on the sequence.

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