A criterion for a monomial in P(3) to be hit

elements. It is a graded left module over the Steenrod algebra A. The hit problem associated to the action of A on P(n) is to find a criterion for a monomial f 2 P(n) of positive degree d to be expressible in the form f = P i Sqi(fi) where Sqi 2 A and fi 2 P(n) have strictly lower grading than d. Such an f is called a hit monomial. The hit elements in the 1-variable and the 2-variable cases have been characterized [see N. E. Steenrod, Cohomology operations, Princeton Univ. Press, Princeton, N.J., 1962; MR0145525 (26 #3056); F. P. Peterson, “Generators of H (RP1 ^RP1) as a module over the Steenrod algebra”, Abstracts Amer. Math. Soc. (1987), Abstract 833-55- 89; per bibl.]. In the paper under review the author is concerned with the hit problem for three variables. He gives necessary and sufficient condition for a monomial in L(3) to be hit, where L(3) is the ideal in P(3) generated by the elementary symmetric function 3 = x1x2x3.