Commutators in Central Products of Cayley-Dickson Loops
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910061883817984 |
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| author | Chapman, Adam Levin, Ilan |
| author_facet | Chapman, Adam Levin, Ilan |
| contents | This paper studies the triviality of commutators in central products of Cayley-Dickson loops. Two immediate outcomes of this study are (1) the construction of a sequence of non-commutative loops in which the chance of a random commutator to be trivial approaches 1, and (2) an easy proof for why if two central products of $n$-fold Cayley-Dickson loops are isomorphic for $n\geq 3$, then the loops in the first product are term-wise isomorphic to the loops in the second product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20495 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Commutators in Central Products of Cayley-Dickson Loops Chapman, Adam Levin, Ilan Rings and Algebras Group Theory Probability 20N05 (primary), 17D99 (secondary) This paper studies the triviality of commutators in central products of Cayley-Dickson loops. Two immediate outcomes of this study are (1) the construction of a sequence of non-commutative loops in which the chance of a random commutator to be trivial approaches 1, and (2) an easy proof for why if two central products of $n$-fold Cayley-Dickson loops are isomorphic for $n\geq 3$, then the loops in the first product are term-wise isomorphic to the loops in the second product. |
| title | Commutators in Central Products of Cayley-Dickson Loops |
| topic | Rings and Algebras Group Theory Probability 20N05 (primary), 17D99 (secondary) |
| url | https://arxiv.org/abs/2603.20495 |