Burkhard Külshammer (Jéna): Loewy lengths of blocks of finite groups and their centers

The group algebra $FG$ of a finite group $G$ over a field $F$ of prime characteristic
$p$ has a unique decomposition into blocks; these are indecomposable ideals and
finite-dimensional algebras. Each block $B$ has a largest nilpotent ideal, its
radical. The Loewy length of $B$ measures how nilpotent the radical is. In my talk
I will first give a survey on known results in the area. Then I will present
recent results by Koshitani, Sambale and myself. I will also report on known
facts concerning the Loewy length of the center of a block and then outline new
developments obtained by Otokita, Sambale and myself.