Genus zero composition factors of Lie rank one
by
Daniel Frohardt
Wayne State University
Coauthors: Robert Guralnick (USC), Kay Magaard (Wayne State)

This talk is based on joint work with R. Guralnick and K. Magaard.

A permutation group G has genus g if it acts as the mondromy group of a covering of the punctured projective complex line by a surface of genus g. Let E(g) be the set of all simple groups S such that S is a composition factor of a group of genus g and S is neither cyclic nor alternating. It is now known that, as conjectured by Guralnick and Thompson in 1990, E(g) is finite for every non-negative integer g. The set E(0) is of particular interest. The majority of simple groups in E(0) are of low Lie rank, and in the majority of cases the related action is on points of the natural module. The goal is to establish this precisely and to do so in a way that sheds light on why it turns out to be true. This work should be seen in the context of furthering that goal.

Date received: March 12, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagg-20.