Date: Mon, 6 Apr 1998 11:05:03 -0400 (EDT) From: Homer BechtellTo: group-pub-forum@maths.bath.ac.uk I apologize for not having responded earlier on the status of the question raised. I. Robert van der Waal suggested the work of Gautam N. Pandya: 1. On automorphisms of finite simple Chevalley groups, J. Number Theory 6, 171-184 (1974). 2. Algebraic groups and automorphisms of finite Chevalley groups, J. Number Theory 6, 239-247 (1974) The first article identifies a collection Of Chevalley groups of the classical types as well as several exceptional types in which Aut(G) splits over INN(G). In the second, it is proven that under suitable restrictions on the base fields this is not always the case. The motivation for these investigations was the article by Bercov. II. Robert Wilson points out that the A6 = L2(9) example generalizes to all L2(q^2) and that U3(8) generalizes to U3(q^3). He conjectures that the property holds for all groups of Lie type in which the diagonal and the field automorphisms have a common factor but he has made no attempt to prove it. One `sporadic' example, the Tits group, is noted also to have the property. III. Derek Holt responded to the second question on whether or not a group in which each composition factor is a nonabelian simple group of fixed type and for which Aut(G) does not split over Inn(G) would necessarily split over each G-chief factor. An example was provided via the twisted wreath product for A6 which does not. He referred to his article "Embeddings of group extensions into wreath products, Quart. J. Math. Oxford 29 (1978), 463-478" for more details.