The intersection of the admissible basis and the Milnor basis of the Steenrod algebra Original Research Article

We prove a conjecture of Monks [4] on the relation between the admissible basis and the Milnor basis of the mod 2 Steenrod algebra A2, and generalise the result to the mod p Steenrod algebra Ap where p is prime. This establishes a necessary and sufficient condition for the Milnor basis element P(r1, r2,…, rk) and the admissible basis element PtPt2 …Ptk to coincide. The main technique used is the ‘stripping’ method which utilises the action of the dual algebra Ap* on Ap.