A Characterization of Semidirect Products

From (ii) we know that s a = (s l)(l a). From Corollary 7.3.4(ii) we also obtain 

It is the purpose of this (short) section to show that the four conditions given in Theorem 7.3.5 are sufficient to identify a scheme as a semidirect product. 

Throughout this section, the letters T and U will stand for closed subsets of S satisfying 1 = T ( U and U C Ns(T). We shall always assume that, for any two elements t in T and u in U, 1 = tu.  

there exists an element u in q p pq such that fay G utapaq n T. 

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