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Jan 7, 2022 at 19:01 comment added Robert Bruner should also mention that, if X is finite CW, then the isomorphism between H_{-k}(DX) and H^k(X) converts Dyer-Lashof operations in the homology of the E_\infty ring spectrum DX = F(X,S) into Steenrod operations in the cohomology of X. (Remark 1.2, p. 60, Springer LNM 1176, H_\infty Ring Spectra ...)
May 4, 2019 at 22:49 history edited Robert Bruner CC BY-SA 4.0
Added example.
Apr 25, 2019 at 15:20 vote accept FKranhold
Apr 25, 2019 at 15:18 comment added Robert Bruner You might also want to look at the work of Pengelley and Williams on the Araki-Kudo (Kudo-Araki?) algebra.
Apr 25, 2019 at 15:15 history edited Robert Bruner CC BY-SA 4.0
'the' -> 'a', since a particular Sylow p-subgroup is most relevant.
Apr 25, 2019 at 14:38 history edited Michael Albanese CC BY-SA 4.0
added 15 characters in body
Apr 25, 2019 at 13:34 history answered Robert Bruner CC BY-SA 4.0