The Local Structure Theorem: The wreath product case

Abstract

Groups with a large p-subgroup, p a prime, include almost all of the groups of Lie type in characteristic p and so the study of such groups adds to our understanding of the finite simple groups. In this article we study a special class of such groups which appear as wreath product cases of the Local Structure Theorem [MSS2]. V = K∈K [V, K] and K = × K∈K K,and, for each K ∈ K, K ∼ = SL 2 (q) and [V, K] is the natural SL 2 (q)-module for K. 2