In this paper, we determine the homotopy groups and for abelian groups by using the following methods from group theory and homotopy theory: derived functors, the Carlsson simplicial construction, the Baues–Goerss spectral sequence, homotopy decompositions and the methods of algebraic –theory. As the applications, we also determine with for some nonabelian groups and , and for the –th alternating group .
"On homotopy groups of the suspended classifying spaces." Algebr. Geom. Topol. 10 (1) 565 - 625, 2010. https://doi.org/10.2140/agt.2010.10.565