Let the mod 2 Steenrod algebra, .4, and the general linear group, GL(fc,F2), act on P_k := F₂[x₁,...,x_k] with |x₁| = 1 in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra D_k := (P_k)^GL(k'F2) is A-decomposable in Pfc for arbitrary k > 2. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in Q₀S⁰ are the elements of Hopf invariant one and those of Kervaire invariant one. ©2001 American Mathematical Society.

Hung N.H.V., Nam T.N.

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