Hypermaps over non-abelian simple groups and strongly symmetric generating sets

Andrea Lucchini¹ ; Pablo Spiga

¹University of Padova

The electronic journal of combinatorics, Tome 30 (2023) no. 3

Résumé

A generating pair $x, y$ for a group $G$ is said to be symmetric if there exists an automorphism $\varphi_{x,y}$ of $G$ inverting both $x$ and $y$, that is, $x^{\varphi_{x,y}}=x^{-1}$ and $y^{\varphi_{x,y}}=y^{-1}$. Similarly, a group $G$ is said to be strongly symmetric if $G$ can be generated with two elements and if all generating pairs of $G$ are symmetric. In this paper we classify the finite strongly symmetric non-abelian simple groups. Combinatorially, these are the finite non-abelian simple groups $G$ such that every orientably regular hypermap with monodromy group $G$ is reflexible.

Détail

DOI : 10.37236/10286

Classification : 20B25, 05C25, 20D05
Mots-clés : strongly symmetric group, regular hypermap, monodromy group