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arxiv: 1608.02727 · v1 · pith:UMUB4J4Gnew · submitted 2016-08-09 · 🧮 math.RT

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

classification 🧮 math.RT
keywords groupscentreintersectionsubgroupssylowtrivialblockfinite
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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.

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