2 problems

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Byott's insolvability conjecture for realizable group pairs
Byott's conjecture. If $(G,N)$ is realizable and $G$ is insolvable, then $N$ is also insolvable.
Conjecturerefutedfinite-groups hopf-galois-structures skew-bracesarXiv posted 2 days ago
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BNY's conjecture on left braces of size $12p$
Let $p$ be a prime, and let $b(12p)$ denote the number of isomorphism classes of left braces of size $12p$ . BNY's conjecture. … This conjecture predicts the number of isomorphism c…
Conjectureopenfinite-groups hopf-galois-structures left-bracesarXiv posted 2 days ago

Byott's insolvability conjecture for realizable group pairs