Year: 2020
Type: preprint
Abstract: The minimal degree of a permutation group $G$ is defined as the minimal number of non-fixed points of a non-trivial element of $G$. In this paper we show that if $G$ is a transitive permutation group of degree $n$ having no non-trivial normal $2$-subgroups such that the stabiliser of a point is a $2$-group, then the minimal degree of $G$ is at least $\frac{2}{3}n$. The proof depends on the classification of finite simple groups.
Source: arXiv (Cornell University)
Authors: Potocnik, Primoz, Spiga, Pablo
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3016594689