Picard groups for blocks with normal defect groups

Abstract: Let $G$ be a finite group, $B$ a $p$-block of $OG$, $O$ a complete DVR. The Picard group of $B$ is the group of auto-Morita equivalences of $B$ and it revealed itself to be a useful tool, for example for dealing with Donovan conjecture. However, it is also interesting in its own right, since it has the structure of a finite group, when $O$ has char 0.

In this talk we will give an introduction to Picard groups for blocks and then present joint work with Livesey on blocks with normal defect groups, providing evidence to a conjecture on basic Morita equivalences.

group theory

Audience: researchers in the topic

Finite Groups in Valencia

Series comments: The seminar meets weekly from February 26th to March 30th 2021.

For a detailed schedule and registration details, please visit the seminar webpage at

sites.google.com/view/finite-groups-seminar2021