  We prove analogues for odd primes of results of Snaith and Barker-Snaith. Let
l denote the p-complete connective Adams summand and consider the group of left
l-module automorphisms of l smash l in the stable homotopy category which
induce the identity on mod p homology. We prove a group isomorphism between
this group and a certain group of infinite invertible upper triangular matrices
with entries in the p-adic integers. We determine information about the matrix
corresponding to the automorphism 1 smash Psi^q, where Psi^q is the Adams
operation and q is an integer which generates the p-adic units.
