The Alperin and Dade Conjectures for Ree Groups2F4(q2) in Non-defining Characteristics

Abstract

This paper is part of a program to study Alperin's weight conjecture and Dade's ordinary conjecture on counting characters in blocks for several finite groups. The local structures of radical subgroups and certain radical 3-chains of a Ree group of typeF4are given and the conjectures and a conjecture of Olsson are confirmed for the group when the characteristic of the modular representation is distinct from the defining characteristic of the group.