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By Frederick R. Cohen

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113 T h e R-algebra s t r u c t u r e of H*SF . . . . . . . . . I 3 1 Homology operations f o r m a t r i x groups . . . . . . . 142 Em ring s p a c e s and the # product Before proceeding to the analysis of t h e i r homological s t r u c t u r e , we m u s t r e c a l l the definition of E General l i n e a r groups of finite fields The homology of BCoker J,B(SF;kO), 13. = 2; . . . . . 148 Bibliography . A : k(k) x &(jl) s t r u c t u r e of on a n E . operad m x..

Rather than u s e the Adem relations t o compute a sti i J Q ( P + Q [I]). i >O On t h e right, = i>o Visibly a S1 . Sk (or Q [I]"'Q [I] if p = 2), w h e r e k = P(1). roof. ] QS[l] = QS QS[l] t as, w h e r e a directly, we observe that, by a n e a s y calculation, the induction hypothesis implies that a primitive. Since a i s a l i n e a r combination of length two elements of R j>O Iterating, we r e a c h t e r m s w h e r e the e r r o r summation i s z e r o a f t e r finitely many steps. i J Since P*Q [I] i s a l i n e a r combination of monomials K Q [I] Thus 2 * i s just t h e t r a n s l a t e of the product the one component.

Ll0 The orthogonal, unitary, and syrnplectic groups m sequences I at p = 2 j = j l . . j k. jk) denote the s e t of a l l = { i l , . i ) such that 1 5 ir (- jr and o r d e r s ( j l , . k lexicographically. I 2 1, l e t S O l , . For j This fixes a n action of For u{il, .... \} u< jl, Z. on S(jl, 3 ...