The strong symmetric genus of the hyperoctahedral groups

Abstract

The strong symmetric genus of a group is the smallest genus of a surface on which the group acts faithfully as a group of orientation preserving automorphisms. In this paper we announce and prove the strong symmetric genus for the hyperoctahedral groups. This parameter is already known for the alternating and symmetric groups as well as the sporadic finite simple groups.

11 pages, 3 figures; fixed typo in Theorem 1