EXTENSIONS OF PERIODIC LINEAR GROUPS WITH FINITE UNIPOTENT RADICAL

This article is published posthumously for the author Richard Phillips. The other authors dedicate this paper to his memory. A group is called p-linear if it is isomorphic to a subgroup of GL(n,K) for some field K of characteristic p and some integer n. Let H be a normal subgroup of G and assume that both H and G/H are periodic and p-linear. In addition, assume that bothH andG/H have finite unipotent radicals and that the Hirsch-Plotkin radical of H is C̆ernikov. The main result of this article is a proof that under these assumptions G is p-linear. An example is provided showing the result is false if the assumption regarding the Hirsch-Plotkin radical is removed. 1 1. Results For finite n, the group G is said to be K-linear of degree n if it is isomorphic to a subgroup of GL(n,K) and is p-linear if it is K-linear for some field K of characteristic p