Components and realizability of fusion systems

Abstract For it is known that a saturated ‐fusion system is realizable if and only if each of its components is realizable by a finite simple group. For primes this is false. Building on work of Broto, Møller, Oliver and Ruiz, we show, however, that a fusion system is realizable if and only if for each of its components there exists a realizable subnormal subsystem of with .