A GENERALIZATION OF THE Z#-THEOREM E. HENKE AND J. SEMERARO
Abstract. Glaubermann's Z#-theorem and analogous statements for odd 
primes show that, for any prime p and any finite group G with Sylow p- 
subgroup S, the centre of G is determined by the fusion system FS(G). Build- 
ing on these results we show a statement that can be considered as a general- 
ization: For any normal subgroup N of G, the centralizer CS(N) is expressed 
in terms of the fusion system FS(G) and its normal subsystem induced by N.