Geodesic
Localization, Algebraic Loops and H-Spaces I
Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 427-435

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If (Y, μ) is an H-Space (here all our spaces are assumed to be finitely generated) with homotopy associative multiplication μ. and X is a finite CW complex then [X, Y] has the structure of a nilpotent group. Using this and the relationship between the localizations of nilpotent groups and topological spaces one can demonstrate various properties of [X,Y] (see [1], [2], [6] for example). If μ is not homotopy associative then [X, Y] has the structure of a nilpotent loop [7], [9]. However this algebraic structure is not rich enough to reflect certain significant properties of [X, Y]. Indeed, we will show that there is no theory of localization for nilpotent loops which will correspond to topological localization or will restrict to the localization of nilpotent groups. 
Shar, Albert O. Localization, Algebraic Loops and H-Spaces I. Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 427-435. doi: 10.4153/CJM-1979-046-8
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