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Hi All,

I would like to know the Automorphism group of some simple classical groups, such as PSL(n,q) or some PSU or PSp groups. Could you please give me some recommended books or papers then? I could not find one.

Thanks in advance.

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Here is a list that contains the orders (but not the structure, which mostly comes from diagram automorphisms): – S. Carnahan Aug 8 '11 at 3:59
up vote 8 down vote accepted

As Tom points out, the Springer survey by Dieudonne (in French) is a standard source, with lots of references to the primary literature since at least the older work of Schreier and van der Waerden. Later work by O'Meara and others has mainly been concerned with more general settings over fields and commutative rings, going in the direction of algebraic K-theory. By now the specific groups mentioned in the question have also been treated in other sources, such as the 2009 Springer graduate text GTM 251 *The Finite Simple Groups" by Robert A. Wilson. There are also some relevant MO discussions, if you search for "automorphism group".

The algebraic group viewpoint on automorphism groups was developed by Steinberg for linear groups over finite fields, while I showed how to adapt those methods to infinite fields in a 1969 paper freely available here.

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That's a very useful addition to my answer indeed! – Tom De Medts Mar 12 '11 at 8:59

Dieudonné's "La Géometrie des Groupes Classiques" might be what you're looking for; it has a whole chapter on automorphisms and isomorphisms of the classical groups.

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