On a theorem of Eilenberg-MacLane
Minoru Nakaoka · Osaka City University (Osaka City University) · 1954
Introducing the notion of 'classes of Abelian groups', J-P. Serre gave in his recent paper [7] very useful generalizations of the classical theorems of W. Hurewicz and of J.H.C. Whitehead. Among the same kind of these classical theorems, we find a theorem due to S. Eilenberg and S. MacLane [4]: If Y is an arcwise connected space with vanishing homotopy groups π_i(Y) for i < n and n < i < q, then the homotopy group π_n(Y) determines the homology groups of Y in dimensions < q, and partially the q-dimensional homology group of Y....