THE INTERSECTION OF THE ADMISSIBLE BASIS AND THE MILNOR BASIS OF THE STEENROD ALGEBRA

We prove a conjecture of Monks [4] on the relation between the admissi ble basis and the Milnor basis of the mod2 Steenrod algebra A(2), and generalise the result to the mod p Steenrod algebra A(p) where p is pr ime. This establishes a necessary and sufficient condition for the Mil nor basis element P(r(1),r(2),...,r(k)) and the admissible basis eleme nt (PPt2)-P-t1...P-tk to coincide. The main technique used is the 'str ipping' method which utilises the action of the dual algebra A(p) on A(p). (C) 1998 Elsevier Science B.V. All rights reserved.