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

Showing 2019Show all

5 papers · 1 filter

math.GR2019

Finite groups with an automorphism that is a complete mapping

Alexander Bors

We show that a finite group $G$ admitting an automorphism $α$ such that the function $G \to G$ , $g \mapsto g α (g)$ , is bijective is necessarily solvable.

math.GR2019★ 1 cited

Documentation for the GAP code file OrbOrd.txt

Alexander Bors, Michael Giudici, Cheryl E. Praeger

We give a comprehensive description of the functions and variables defined in the authors' GAP code file OrbOrd.txt, which serve mainly to compute (bounds on) the number of $\opera…

math.GR2019

Finite groups with only small automorphism orbits

Alexander Bors

We study finite groups $G$ such that the maximum length of an orbit of the natural action of the automorphism group $Aut (G)$ on $G$ is bounded from above by a consta…

math.GR2019

Automorphism orbits and element orders in finite groups: almost-solubility and the Monster

Alexander Bors, Michael Giudici, Cheryl E. Praeger

For a finite group $G$ , we denote by $ω (G)$ the number of $Aut (G)$ -orbits on $G$ , and by $o (G)$ the number of distinct element orders in $G$ . In this…

math.GR2019

Words, permutations, and the nonsolvable length of a finite group

Alexander Bors, Aner Shalev

We study the impact of certain identities and probabilistic identities on the structure of finite groups. More specifically, let $w$ be a nontrivial word in $d$ distinct variables…