A divisibility relation is proved connecting the invariant factors of integral matrices A, B, C when C = AB. Let A, B, and CbenX n matrices with entries in a principal ideal domain 31, and with C -AB. In a recent note [3] on the multiplicative property of the Smith normal form, Morris Newman observed the fact: if d¡(A) denotes the z'th determinantal divisor of A, then di(A)di(B) \ dt(C), where | denotes divisibility. The objective of this paper is to prove the following divisibility property of

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... invariant factors, a property containing Newman's observation as a special case. Notation. ax\a2\ -■ -\an, ßx\ß2\ ■■ -\ßn, yx\y2\ ■■ -\yn axe the invariant factors of A, B, and C, respectively. See [4] for all properties of invariant factors used here. Theorem. We have