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To any block idempotent $b$ of a group algebra $kG$ of a finite group $G$over a field $k$ of characteristic $p>0$, Puig associated a fusion system andproved that it is saturated if the $k$-algebra $kC_G(P)e$ is split, where$(P,e)$ is a maximal $kGb$-Brauer pair. We investigate in the non-split casehow far the fusion system is from being saturated by describing it in anexplicit way as being generated by the fusion system of a related blockidempotent over a larger field together with a single automorphism of thedefect group.

Fusion systems of blocks of finite groups over arbitrary fields