Alexander Bors

activity

20142023

most citedClassification of finite group automorphisms with a large cycle

4 citations · 14 across the 21 of their papers we have counts for

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Showing 2015Show all

4 papers · 1 filter

math.GR2015★ 1 cited

A bound on element orders in the holomorph of a finite group

Alexander Bors

Let $G$ be a finite group. We prove a theorem implying that the orders of elements of the holomorph $Hol (G)$ are bounded from above by $∣ G ∣$ , and we discuss an appli…

math.GR2015

Finite groups with an automorphism of large order

Alexander Bors

Let $G$ be a finite group, and assume that $G$ has an automorphism of order at least $ρ ∣ G ∣$ , with $ρ \in (0, 1)$ . Generalizing recent analogous results of the author on fin…

math.GR2015★ 1 cited

On finite groups where the order of every automorphism is a cycle length

Alexander Bors

Using Frobenius normal forms of matrices over finite fields as well as the Burnside Basis Theorem, we give a direct proof of Horoševskiĭ's result that every automorphism $α$ of a f…

math.GR2015★ 3 cited

Cycle lengths in finite groups and the size of the solvable radical

Alexander Bors

We prove the following: For any $ρ \in (0, 1)$ , if a finite group $G$ has an automorphism with a cycle of length at least $ρ \cdot ∣ G ∣$ , then the index of the solvable radica…