Date: Mon, 6 Apr 1998 11:05:03 -0400 (EDT)
From: Homer Bechtell 
To: 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.