On Finite Groups of Symmetries of Surfaces

Abstract

The genus spectrum of a finite group $G$ is the set of all $g\ge 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating the genus spectrum of $G$ to its group theoretical properties. In particular, the arithmetical properties of genus spectra are discussed, and explicit results are given on the 2-groups of maximal class, certain sporadic simple groups and a some of the groups PSL$(2,q)$, where $q$ is a small prime power. These results are partially new, and obtained through both theoretical reasoning and application of computational techniques.

arXiv comment24 pages. Changed title and abstract from premature first version

References in corpus (1)

• On p-groups of Gorenstein-Kulkarni type