## The Homology of Iterated Loop Spaces |

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action acts additive admissible allowable analogous apply argument assume basis Bockstein calculation Cartan formula classes Clearly cohomology commutative complete component composite conjugation connected Consequently consider construction Corollary course D-space decomposable defined definition denote described determined diagram elements equivalence evident fact fibration fixed give given hence hold homology homology operations homotopy Hopf algebra identity immediate implies inclusion induction infinite loop spaces isomorphism Lemma Math modulo monomials morphism natural non-zero Note observe obtain obvious operad operations prime primitive Proof Proof of Theorem properties Proposition prove Recall Remark restriction result ring specified spectral sequence Steenrod structure summand Theorem trivial VIII write zero