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Left braces of size $p^2(2p+1)^2$, for $p$ an odd Germain prime

Teresa Crespo
Jan 2024
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摘要原文
We consider relatively prime integer numbers $m$ and $n$ such that each 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 $p$ an odd Germain prime and $q=2p+1$.
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