SMS scnews item created by Anthony Henderson at Fri 8 Aug 2008 1548
Type: Seminar
Distribution: World
Expiry: 19 Aug 2008
Calendar1: 19 Aug 2008 1605-1655
CalLoc1: Carslaw 251
CalTitle1: Algebra Seminar: Glasby -- The automorphisms of p-groups with only three characteristic subgroups
Auth: anthonyh@asti.maths.usyd.edu.au

Algebra Seminar

The automorphisms of p-groups with only three characteristic subgroups

Stephen Glasby

19th August, 4:05-4:55pm, Carslaw 251 (***SPECIAL DAY, TIME AND ROOM***)


Abstract

Although there are p^{2n^3/27} groups G of order p^n (by work of Higman and Sims), and Aut(G) can have arbitrary quotients (by work of Heineken and Liebeck), most p-groups G have very small automorphism groups (by Helleloid and Martin). This talk considers p-groups G where G, Phi(G) and 1 are the only characteristic subgroups. These groups seem to have large and interesting automorphism groups seemingly related to maximal irreducible linear groups. Their study raises questions about the representation theory of exterior squares. This is joint work with Csaba Schneider and Peter Pálfy.


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