The nonabelian product modulo sum
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arXiv
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909861567004672 |
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| author | Corson, Samuel M. |
| author_facet | Corson, Samuel M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_02682 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The nonabelian product modulo sum Corson, Samuel M. Group Theory Logic 03E75, 20A15, 55Q52 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. |
| title | The nonabelian product modulo sum |
| topic | Group Theory Logic 03E75, 20A15, 55Q52 |
| url | https://arxiv.org/abs/2206.02682 |