Sub-Hopf-algebras of the Steenrod algebra

Abstract

In (3) the second author has shown that all sub-Hopf-algebras of the mod 2 Steenrod algebra have a certain form; this resulthas been used in (1) and (2). The analogous result for the mod p Steenrod algebra, where p is an odd prime, is contained in (6). The object of this paper is to give a shorter proof of a slightly sharper result; we construct all the subalgebras in question. In the mod 2 case this sharper result has also been obtained by Anderson and Davis (2).