Geodesic
Homotopy groups as centres of finitely presented groups
Izvestiya. Mathematics , Tome 77 (2013) no. 3, pp. 581-593

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For every finite Abelian group $A$ and integer $n\geqslant 3$ we construct a finitely presented group defined by explicit generators and relations such that its centre is isomorphic to $\pi_n(\Sigma K(A,1))$.
Keywords: homotopy theory, homotopy groups, simplicial groups, finitely presented groups. 
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     author = {J. Wu and R. V. Mikhailov},
     title = {Homotopy groups as centres of finitely presented groups},
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J. Wu; R. V. Mikhailov. Homotopy groups as centres of finitely presented groups. Izvestiya. Mathematics , Tome 77 (2013) no. 3, pp. 581-593. http://geodesic.mathdoc.fr/item/IM2_2013_77_3_a8/