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Let Ps be the mod-2 cohomology of the elementary abelian group (Z/2Z) x • ■ • x (Z/2Z) (s factors). The mod-2 Steenrod algebra A acts on Ps according to well-known rules. If A C A denotes the augmentation ideal, then we are interested in determining the image of the action A ® Ps -* Ps: the space of elements in Ps that are hit by positive dimensional Steenrod squares. The problem is motivated by applications to cobordism theory [PI] and the homology of the Steenrod algebra [S]. Our main result,doi:10.1090/s0002-9939-1991-1045150-9 fatcat:w6m6moi2qzeizpkyy5i5i6uk5q