2 problems

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Uniform generation conjecture for minors of finite abelian p-groups
Uniform generation conjecture. There is a $k\in\mathbb{N}$ such that $\mathcal O_{\mathbf{A},\mathbf{R}}$ is uniformly generated by $k$ -ary $(\mathbf{A},\mathbf{R})$ -minors.
Conjectureopenclonoids finite-groups module-theoryarXiv posted 2 days ago
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Finiteness conjecture for clonoids between finite modules
Finiteness conjecture. There are only finitely many clonoids from $\mathbf{A}$ to $\mathbf{B}$ if and only if $\mathbf{A}$ and $\mathbf{B}$ are of coprime order.
Conjectureopenclonoids finite-modules universal-algebraarXiv posted 2 days ago

Uniform generation conjecture for minors of finite abelian p-groups