Speaker: Inga Schwabrow (Kaiserslautern)
Title: Centres of Blocks of Finite Groups with Trivial Intersection Sylow p-Subgroups
Abstract:
Let \(G\) be a finite group, \(k\) an algebraically closed field of characteristic \(p\), and let \(B_0\) denote the principal block of \(kG\). If any two distinct Sylow \(p\)-subgroups of \(G\) intersect trivially, then it is well known that there exists a stable equivalence of Morita type between \(B_0\) and its Brauer correspondent \(b_0\) in \(kN_G(P)\). In this talk, I will give a brief overview of how the analysis of the Loewy structure of the centre of \(B_0\) and \(b_0\) respectively allows us to deduce that this stable equivalence of Morita type does not always induce an algebra isomorphism between the two centres. As a consequence, an analogue of Broué's abelian defect group conjecture does not hold for these groups.