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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2401.16892 |
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| _version_ | 1866913684139278336 |
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| author | Crespo, Teresa |
| author_facet | Crespo, Teresa |
| contents | We consider relatively prime integer numbers $m$ and $n$ such that each solvable group of order $mn$ has a normal subgroup of order $m$. We prove that each brace of size $mn$ is a semidirect product of a brace of size $m$ and a brace of size $n$. We further give a method to classify braces of size $mn$ from the classification of braces of sizes $m$ and $n$. We apply this result to determine all braces of size $p^2q^2$, for $p$ and $q$ odd primes satisfying some conditions which hold in particular for $p$ a Germain prime and $q=2p+1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16892 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Left braces of size $p^2q^2$ Crespo, Teresa Group Theory Quantum Algebra 16T25, 20D20, 20D45 We consider relatively prime integer numbers $m$ and $n$ such that each solvable group of order $mn$ has a normal subgroup of order $m$. We prove that each brace of size $mn$ is a semidirect product of a brace of size $m$ and a brace of size $n$. We further give a method to classify braces of size $mn$ from the classification of braces of sizes $m$ and $n$. We apply this result to determine all braces of size $p^2q^2$, for $p$ and $q$ odd primes satisfying some conditions which hold in particular for $p$ a Germain prime and $q=2p+1$. |
| title | Left braces of size $p^2q^2$ |
| topic | Group Theory Quantum Algebra 16T25, 20D20, 20D45 |
| url | https://arxiv.org/abs/2401.16892 |