Alexander Bors

activity

20162021

most citedDocumentation for the GAP code file OrbOrd.txt

1 citations · 1 across the 6 of their papers we have counts for

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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 $G$ …

math.GR2020

Finite transitive permutation groups with only small normaliser orbits

Alexander Bors, Michael Giudici

We study finite transitive permutation groups $G ⩽ Sym (Ω)$ such that all orbits of the conjugation action on $G$ of the normaliser of $G$ in $\operatorname{Sym…

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…