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 both H and G/H have finite unipotent radicals and that the Hirsch-Plotkin radical of G/H is Cernikov. 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.
The authors would like to thank Burt Wehrfritz for pointing out that Theorem 1.5 in the published version of this paper is wrong. This mistake has been corrected in the files available here.
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Last Revised 8/25/05