BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Elementary abelian subgroups: From algebraic groups to finite grou
 ps - Alastair Litterick\, University of Essex
DTSTART:20240306T163000Z
DTEND:20240306T173000Z
UID:TALK210862@talks.cam.ac.uk
CONTACT:Adam Jones
DESCRIPTION:Across group theory\, elementary abelian subgroups arise natur
 ally in many contexts. For instance\, they play an important role in modul
 ar representation theory\, in local structure of groups\, and in the cohom
 ology theory of various spaces.This talk will present joint work with Jian
 bei An (University of Auckland) and Heiko Dietrich (Monash University\, Me
 lbourne)\, in which we consider elementary abelian subgroups of reductive 
 algebraic groups in positive characteristic. In contrast with previous wor
 ks which proceed ‘bottom up’\, beginning with elements of order p\, th
 en elements of order p in their centralisers\, and so on\, we use a ‘top
 -down’ approach building on work of R. Griess on maximal elementary abel
 ian subgroups and their normaliser structure. Such subgroups behave differ
 ently depending on whether or not they are toral (contained in a torus)\, 
 and our results are two-fold. For toral subgroups\, we give an efficient c
 ombinatorial algorithm for enumerating subgroups and determining their nor
 maliser and centraliser structure. For non-toral subgroups\, we complement
  work of J. Yu and Andersen et. al.\, and end up with a complete classific
 ation of subgroups which is independent of the ambient characteristic. The
  eventual aim is to use these results to prove local structure results in 
 finite groups of Lie type\, via the Lang-Steinberg theorem\; I will close 
 with a discussion of the subtleties arising in this process.
LOCATION:MR12
END:VEVENT
END:VCALENDAR