Verifying Huppert's Conjecture for PSL₃(q) and PSU₃(q²)

Abstract

Let G be a finite group and cd(G) be the set of irreducible character degrees of G. Bertram Huppert conjectured that if H is a finite nonabelian simple group such that cd(G) = cd(H), then G ≅ H × A, where A is an abelian group. We examine arguments to verify this conjecture for the simple groups of Lie type of rank two. To illustrate our arguments, we extend Huppert's results and verify the conjecture for the simple linear and unitary groups of rank two.

Key Words:

• Character degrees
• Linear groups
• Simple groups
• Unitary groups

2000 Mathematics Subject Classification:

• Primary 20C15
• Secondary 20C33

ACKNOWLEDGMENTS

The author would like to express his sincere thanks to the referee for providing a simpler method for the elimination of the simple groups of Lie type from consideration as well as for the helpful comments and suggestions throughout the manuscript. The author also acknowledges Donald White for his guidance through the research and development of these methods as well as Mark Lewis and Stephen Gagola, Jr., for their suggestions.

Notes

Communicated by A. Turull.