Vadim E. Levit

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20242026

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math.GR2026

Higher Commutativity in Finite Groups, Rigidity, Extremal bounds, and Heisenberg-Type Families

Vadim E Levit, Robert Shwartz

For a finite group $G$ and an integer $r \geq 2$ let $P_{r} (G) := \frac{∣ H o m ( Z ^{r} , G ) ∣}{∣ G ∣ ^{r}},$ where $\Hom(\mathbb Z^r,G)$ is the set of pairwise commuting $r$ -tuples in $G$ .…

math.GR2026

Higher Commutativity in Finite Groups: Exact Asymptotics and Finite Spectrum

Vadim E. Levit, Robert Shwartz

For a finite group G, we study the higher commuting probabilities, namely the probabilities that r randomly chosen elements of G commute pairwise, together with the corresponding n…