D. Dona

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math.GR2025

A CFSG-free explicit Jordan's theorem over arbitrary fields

Jitendra Bajpai, Daniele Dona

We prove a version of Jordan's classification theorem for finite subgroups of $GL_{n} (K)$ that is at the same time quantitatively explicit, CFSG-free, and valid for arbitr…

math.GR2025

Products of three conjugacy classes in the alternating group

Daniele Dona

We prove that for $I^´$ small, $n$ large, and any three conjugacy classes $C_{1}, C_{2}, C_{3}$ of $G = Alt (n)$ of size at least $∣ G ∣^{1 - I^´}$ we have $C_{1} C_{2} C_{3} = G$ . The r…

math.GR2024

Growth estimates and diameter bounds for untwisted classical groups

Babai's conjecture states that, for any finite simple non-abelian group $G$ , the diameter of $G$ is bounded by $(lo g ∣ G ∣)^{C}$ for some absolute constant $C$ . We prove that, for an…

math.GR2024

Writing finite simple groups of Lie type as products of subset conjugates

Daniele Dona

The Liebeck-Nikolov-Shalev conjecture [LNS12] asserts that, for any finite simple non-abelian group $G$ and any set $A \subseteq G$ with $∣ A ∣ \geq 2$ , $G$ is the product of at most $…