Skew braces of size pq
| Autor: | Emiliano Acri, Marco Bonatto |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Algebra and Number Theory
Degree (graph theory) Yang–Baxter equation Mathematics::Number Theory Mathematics::Rings and Algebras 010102 general mathematics Skew Group Theory (math.GR) Mathematics - Rings and Algebras 010103 numerical & computational mathematics 01 natural sciences Brace Combinatorics 16T25 Rings and Algebras (math.RA) Mathematics::K-Theory and Homology Mathematics::Category Theory Mathematics::Quantum Algebra Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) 0101 mathematics Mathematics - Group Theory Mathematics |
| Zdroj: | Communications in Algebra. 48:1872-1881 |
| ISSN: | 1532-4125 0092-7872 |
| DOI: | 10.1080/00927872.2019.1709480 |
| Popis: | We construct all skew braces of size $pq$ (where $p>q$ are primes) by using Byott's classification of Hopf--Galois extensions of the same degree. For $p\not\equiv 1 \pmod{q}$ there exists only one skew brace which is the trivial one. When $p\equiv 1 \pmod{q}$, we have $2q+2$ skew braces, two of which are of cyclic type (so, contained in Rump's classification) and $2q$ of non-abelian type. 9 pages. Final version, accepted for publication in Communications in Algebra. arXiv admin note: text overlap with arXiv:1912.11889 |
| Databáze: | OpenAIRE |
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