Centres of blocks of finite groups with trivial intersection Sylow $p$-subgroups

Abstract

For finite groups $G$ with non-abelian, trivial intersection Sylow $p$-subgroups, the analysis of the Loewy structure of the centre of a block allows us to deduce that a stable equivalence of Morita type does not induce an algebra isomorphism between the centre of the principal block of $G$ and the centre of the Brauer correspondent. This was already known for the Suzuki groups; the result will be generalised to cover more groups with trivial intersection Sylow $p$-subgroups.

9 pages

References in corpus (2)

• Broue's Abelian Defect Group Conjecture for the Tits Group
• On Centres of 3-blocks of the Ree groups ${}^2{G}_2(q)$