2 problems

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The non-abelian kernel conjecture for covers of minimax groups
Let $G$ be a group and consider the covering constructed in the proof of Theorem 1.13. The construction involves a subgroup $X$ and an epimorphism … The kernel is abelian only if…
Conjectureopengroup-covers group-theory minimax-groupsarXiv posted 3 days ago
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Lucchini–Detomi conjecture on non-abelian sigma-primitive groups
Let $G$ be a finite group. Call $G$ $\sigma$ -primitive if $\sigma(G)<\sigma(G/N)$ for every non-trivial normal subgroup $N$ of $G$ , where $\sigma(G)$ is the least number of proper…
Conjectureopenfinite-groups group-coversarXiv posted 3 days ago

The non-abelian kernel conjecture for covers of minimax groups