Supersingular abelian varieties over finite fields

Let A be a supersingular abelian variety defined over a finite field k. We give an approximate description of the structure of the group A(k) of k-rational points of A in terms of the characteristic polynomial f of the Frobenius endomorphism of A relative to k. Write f = Pi g(i)(ei) for distinct monic irreducible polynomials g(i) and positive integers e(i). We show that there is a group homomorphism phi: A(k) --> Pi (Z/g(i)(1) Z)(ei) that is "almost" an isomorphism in the sense that the sizes of the kernel and the cokernel of phi are bounded by an explicit function of dim A. (C) 2001 Academic Press.