Let D be the defect group of a p-block of a finite group G. Let P, Q be two p-Sylow groups of G containing D. Then there exist x, y, z E CG(Z) such that: (i) z is p-regular and D is a p-Sylow group of CG(Z); (ii) D = QX n P = Q n PY; and (iii) z = xy. This refines an earlier theorem of J. A. Green. Let D be the defect group of a p-block of a finite group G. If P is a p-Sylow group of G containing D, it has been known for some time that there must exist another p-Sylow group Q such that P n Q = D. This so-called 'Sylow intersection' property was first established by Green [2] using vertex theory, and later also proved by Thompson [4] using Brauer's methods. In [1, p. 241] Alperin indicated, that D can even be expressed as a tame intersection of two suitable p-Sylow groups of G. In 1968, a much more accurate result was obtained by Green [3]. If P is any given p-Sylow group of G containing D, Green proved that there must exist x, y, z E CG(D) such that (i) z is p-regular and D is a p-Sylow group of CG(z); (ii) D = P n PX = p n PY; (iii) z = xy. In particular, if P is chosen such that Np(D) is a p-Sylow group of NG(D), then D = P n PX in (ii) clearly expresses D as a tame Sylow intersection. On the other hand, the conclusion of (i) recaptures the earlier result of Brauer that D must be a class-defect group of some p-regular conjugacy class in G. Green's proof of the above result is a rather elaborate (but extremely successful) application of vertex theory, in the more general framework of Galgebras [3]. For Z a sufficiently large P-adic ring (plj), Green views the integral group ring r = DG as a (left) G x G-algebra via the action (gl, g2) * y = g1 Yg2 1 (gi G G, y G r). Let E E r be the p-adic idempotent associated with the given p-block, whose defect group is D. Given a p-Sylow group P D D, the following steps are important ingredients in Green's proof: (1) The vertex of the indecomposable Z(G x G)-module rF E is A(D) = {(d,d): d e D}. (2) When viewed as Z(P x P )-module by restriction, r . E has at least one indecomposable constituent with vertex = A(D) C P x P. (3) Let Uwc PwP be the (P,P)-double coset decomposition of G, and let [PwP] denote the Z(P x P)-submodule of r, with PwP as ?-basis. Then, Received by the editors November 22, 1974. AMS (MOS) subject classiylcations (1970). Primary 20C20, 20D20.