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This research demonstrates conditions under which fusion systems are realizable, with implications for group theory.
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 .
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Henke et al. (2026) studied this question.
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