Summary: The question of whether or not the product of two nonsingular n-by-n M-matrices has a nested sequence of positive principal minors (abbreviated to a nest) is considered. For n = 2, 3, 4 such a product always has a nest, and this is conjectured for n = 5. For general n, examples of products of two M-matrices with specified structure are identified as having a leading or trailing nest. For n = 4, it is shown that the cube of an M-matrix need not have a nest.

15A15

M-matrix, nested sequence of principal minors, P -matrix