Group in which the ZJ-functor controls fusion for a prime
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Suppose is a finite group and is a prime number. We say that is a group in which the ZJ-functor controls fusion for if the ZJ-functor, viewed as a conjugacy functor on , controls fusion in with respect to . In other words, given a -Sylow subgroup of and two subsets of that are conjugate in , the subsets are conjugate in .