Les personnes qui possèdent un compte PLM-Mathrice sont invités à l'utiliser.

# Colloque 2016 du GDR 2875, Topologie Algébrique et Applications

11-14 octobre 2016
Europe/Paris timezone
Accueil > Timetable > Contribution details

# Contribution Invited speaker

Topologie algébrique et applications

# Local structure of finite groups and their p-completed classifying spaces

## Intervenant(s)

• Prof. Bob OLIVER

## Content

I plan to describe the close connection between the homotopy theoretic properties of the $p$-completed classifying space of a finite group $G$ and the $p$-local group theoretic properties of $G$. One way in which this arises is in the following theorem originally conjectured by Martino and Priddy: for finite groups $G$ and $H$, $BG{}^\wedge_p\simeq BH{}^\wedge_p$ if and only if $G$ and $H$ have the same $p$-local structure (the same conjugacy relations among $p$-subgroups). Another involves a description, in terms of the $p$-local properties of $G$, of the group $\mathrm{Out}(BG{}^\wedge_p)$ of homotopy classes of self equivalences of $BG{}^\wedge_p$.

After describing the general results, I'll give some examples and applications of both of these, especially in the case where $G$ and $H$ are simple Lie groups over finite fields.