A generalization of Ito's theorem to skew braces
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929198756528128 |
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| author | Tsang, Cindy |
| author_facet | Tsang, Cindy |
| contents | The famous theorem of Itô in group theory states that if a group $G=HK$ is the product of two abelian subgroups $H$ and $K$, then $G$ is metabelian. We shall generalize this to the setting of a skew brace $(A,{\cdot\,},\circ)$. Our main result says that if $A = BC$ or $A = B\circ C$ is the product of two trivial sub-skew braces $B$ and $C$ which are both left and right ideals in the opposite skew brace of $A$, then $A$ is meta-trivial. One can recover Itô's Theorem by taking $A$ to be an almost trivial skew brace. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_10081 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A generalization of Ito's theorem to skew braces Tsang, Cindy Group Theory Quantum Algebra Rings and Algebras The famous theorem of Itô in group theory states that if a group $G=HK$ is the product of two abelian subgroups $H$ and $K$, then $G$ is metabelian. We shall generalize this to the setting of a skew brace $(A,{\cdot\,},\circ)$. Our main result says that if $A = BC$ or $A = B\circ C$ is the product of two trivial sub-skew braces $B$ and $C$ which are both left and right ideals in the opposite skew brace of $A$, then $A$ is meta-trivial. One can recover Itô's Theorem by taking $A$ to be an almost trivial skew brace. |
| title | A generalization of Ito's theorem to skew braces |
| topic | Group Theory Quantum Algebra Rings and Algebras |
| url | https://arxiv.org/abs/2305.10081 |