2 problems

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Degree of commutativity characterizes virtually abelian groups
Degree-of-commutativity conjecture.
Conjectureopencommutativity group-theory virtually-abelian-groupsarXiv posted 2 days ago
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Antolín–Martino–Ventura conjecture on degree of commutativity in exponential-growth groups
Let $G$ be a finitely generated group of exponential word growth, and let $S$ be a finite generating set of $G$ . Antolín–Martino–Ventura conjecture. Then … irrespective of the choi…
Conjectureopencommutativity group-theory growth-of-groupsarXiv posted 2 days ago

Degree of commutativity characterizes virtually abelian groups