COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Algebra and Representation Theory Seminar > Elementary abelian subgroups: From algebraic groups to finite groups

## Elementary abelian subgroups: From algebraic groups to finite groupsAdd to your list(s) Download to your calendar using vCal - Alastair Litterick, University of Essex
- Wednesday 06 March 2024, 16:30-17:30
- MR12.
If you have a question about this talk, please contact Adam Jones. Across group theory, elementary abelian subgroups arise naturally in many contexts. For instance, they play an important role in modular representation theory, in local structure of groups, and in the cohomology theory of various spaces.This talk will present joint work with Jianbei An (University of Auckland) and Heiko Dietrich (Monash University, Melbourne), in which we consider elementary abelian subgroups of reductive algebraic groups in positive characteristic. In contrast with previous works which proceed ‘bottom up’, beginning with elements of order p, then 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 abelian subgroups and their normaliser structure. Such subgroups behave differently 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 combinatorial algorithm for enumerating subgroups and determining their normaliser and centraliser structure. For non-toral subgroups, we complement work of J. Yu and Andersen et. al., and end up with a complete classification 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. This talk is part of the Algebra and Representation Theory Seminar series. ## This talk is included in these lists:- Algebra and Representation Theory Seminar
- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Hanchen DaDaDash
- Interested Talks
- MR12
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsPhotonics Summer Seminars 2017 IfM Research Capability Development Programme Seminar Series Rouse Ball Lectures## Other talksInteraction between fast tides and convection How storm develops as the wind blows Photoevaporation from Exoplanet Atmospheres: Understanding the Role of Stellar Winds and Considering Water-rich Atmospheres Estimating Food Waste Produced by the Public Sector Novel processing and 3D correlative imaging of electrodes for batteries The genetic basis of a recent transition to live-bearing in marine snails |