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Win) V2\ | 0 < m, 0 < a < 2\ 3 < n, n ^ 2«] . 2), I 0 < m, 0 < a < 2 6 , 3 < n, n ^ 2*]) = ^2 [^f2m, Ul%h, U$n | 0 < m, 0 < a < 2>, 3 < n, n ^ 2«] . • 7 O n t h e I m a g e of 7rf in 0% Let p : S —> MSp denote the unit of the ring spectrum MSp. Let 'E*yt denote the classical mod two Adams spectral sequence for 7rf. Then p induces a map of Adams spectral sequences pr : ' E**1 —> £*•', 2 < r < oo. ^. The canonical map MSp —> MSU induces an isomorphism Image p^ = Image [//' : S —> MSU], and Image p!

Rf : a £ irf has order 16, 7j2at = 4{3t in ImJ, T]2 G < 2,77,2 > and v2 6 < 7/,//, 77 >. 2, we use the latter Toda bracket and the order of a. The latter three facts are used to derive the differentials and nontrivial extensions given by multiplying by 2, 77 and // in Section 8. We will use the following notation throughout this paper. respectively. (a -f b)\/a\b\. Let 7 # J denote concatenation of sequences. MSP, Let (a, b) denote the binomial coefficient For % an augmented A'-algebra, let % = Cokernel [77 : K —* T] with e : % —> T the canonical projection.

Let a : MSp —> MO and let z, j , />, i', j ' , p' below be the canonical maps. All homology below has ^-coefficients, and PH*X the set of elements of H+X which are 21*-primitive. Then the following diagram commutes: 31 denotes STANLEY 0 . 1) PHkMSp = E^°- HkMSp • <*2 • PHkMO = 'E? 2) From [6] and the Thom isomorphism theorem, we see that any set of polynomial generators of HmMSp maps under a # to the set of fourth powers of a set of polynomial generators of HmMO. For m > 1, define U2m so that h(U2m)4 = a # »(Vi f2 m-i).

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