On finite simple groups of p-local rank two

Baoshan Wang

Vol. 243 (2009), No. 2, 375–398

DOI: 10.2140/pjm.2009.243.375

Abstract

G. Robinson introduced the group invariant known as the p-local rank to study Dade’s conjecture and Alperin’s conjecture. It is known that, for a finite p-solvable group with trivial maximal normal p-subgroup, the p-local rank is greater than or equal to the p-rank. Along those lines, we study the p-local rank of finite simple groups, giving a group-theoretic characterization of finite simple groups having p-local rank two. These results are also necessary for the investigation of such conjectures for finite groups of p-local rank two.

Keywords

p-local rank, finite simple group

Mathematical Subject Classification 2000

Primary: 20C20, 20D06, 20F22, 20E32

Milestones

Received: 14 December 2008

Revised: 25 March 2009

Accepted: 25 March 2009

Published: 1 December 2009