SMALL SUBALGEBRAS OF STEENROD AND MORAVA STABILIZER ALGEBRAS

Let P(j) (resp. S(n)((j))) be the subalgebra of the Steenrod algebra A (p) (resp. nth Morava stabilizer algebra) generated by reduced powers Pp(i), 0 less than or equal to i less than or equal to j (resp. t(i), 1 less than or equal to i less than or equal to j). In this paper we i dentify the dual P(j - 1) of P(j - 1) (resp. S(n)((j)), for j less th an or equal to n) with some Frobenius kernel (resp. F(p)n-points) of a unipotent subgroup G(j + 1) of the general linear algebraic group GL( j+1). Using these facts: we get the additive structure of H(P(1)) = E xt(P(1)) (Z/p, Z/p) for odd primes.