Geodesic
Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 465-470.

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Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of $\Omega \Sigma K(\mathbb{Z}, 2d)$, and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same $n$-type problems and giving us an information about the rational homotopy equivalence.
Classification : 55P62, 55Q15, 55S37
Keywords: Lie bracket; tensor algebra; rationalization; Steenrod power 
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     title = {Homomorphic images and rationalizations based on the {Eilenberg-MacLane} spaces},
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Lee, Dae-Woong. Homomorphic images and rationalizations based on the Eilenberg-MacLane spaces. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 2, pp. 465-470. http://geodesic.mathdoc.fr/item/CMJ_2005__55_2_a15/