Cohomology of the Steenrod algebra mod nilpotents

AbstractPalmieri [Ann. of Math. 149 (1999) 421] gave a complete general description of the cohomology of the Steenrod algebra modulo nilpotent elements. He described several families of explicit elements. We prove that the only elements in filtrations 2 and 3 are those in Palmieri's explicit families. We give conjectures about filtrations 4, 5, 6, and 7