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

collaborators

31 papers

math.NT2023★ 1 cited

Functional graphs of generalized cyclotomic mappings of finite fields

Alexander Bors, Daniel Panario, Qiang Wang

The functional graph of a function $g : X \to X$ is the directed graph with vertex set $X$ the edges of which are of the form $x \to g (x)$ for $x \in X$ . Functional grap…

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.NT2021

Coset-wise affine functions and cycle types of complete mappings

Alexander Bors, Qiang Wang

Let $K$ be a finite field of characteristic $p$ . We study a certain class of functions $K \to K$ that agree with an $F_{p}$ -affine function $K \to K$ on each c…

math.NT2021★ 1 cited

Cycle types of complete mappings of finite fields

Alexander Bors, Qiang Wang

We derive several existence results concerning cycle types and, more generally, the "mapping behavior" of complete mappings. Our focus is on so-called first-order cyclotomic mappin…

math.NT2021

Generalized cyclotomic mappings: Switching between polynomial, cyclotomic, and wreath product form

Alexander Bors, Qiang Wang

This paper is concerned with so-called index $d$ generalized cyclotomic mappings of a finite field $F_{q}$ , which are functions $F_{q} \to F_{q}$ that ag…

math.GR2021

Orbits of Sylow subgroups of finite permutation groups

John Bamberg, Alexander Bors, Alice Devillers +3

We say that a finite group $G$ acting on a set $Ω$ has Property $(*)_{p}$ for a prime $p$ if $P_{ω}$ is a Sylow $p$ -subgroup of $G_{ω}$ for all $ω \in Ω$ and Sylow $p$ -subgroups $P$ of $G$ …