Alexander Bors

activity

20142023

most citedClassification of finite group automorphisms with a large cycle

4 citations · 11 across the 9 of their papers we have counts for

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7 papers · 1 filter

math.GR2022

Compositions and parities of complete mappings and of orthomorphisms

Alexander Bors, Qiang Wang

We determine the permutation groups $P_{comp} (F_{q}), P_{orth} (F_{q}) \leq Sym (F_{q})$ generated by the complete mappings, respec…

math.GR2016

Fibers of automorphic word maps and an application to composition factors

Alexander Bors

In this paper, we study the fibers of "automorphic word maps", a certain generalization of word maps, on finite groups and on nonabelian finite simple groups in particular. As an a…

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…

math.GR2014★ 1 cited

On the endomorphism monoids of some groups with abelian automorphism group

Alexander Bors

We investigate the endomorphism monoids of certain finite $p$ -groups of order $p^{8}$ first studied by Jonah and Konvisser in 1975 as examples for finite $p$ -groups with abelian auto…

math.GR2014★ 4 cited

Classification of finite group automorphisms with a large cycle

Alexander Bors

Let $ψ$ be a permutation of a finite set $X$ . We define $λ (ψ)$ to be the largest fraction of elements of $X$ lying on a single cycle of $ψ$ . For a finite group $G$ , we define $λ(G)…