Homotopy groups as centers of finitely presented groups

TL;DR

This paper constructs finitely presented groups whose centers are homotopy groups of certain topological spaces, linking algebraic group theory with algebraic topology.

Contribution

It provides explicit finitely presented groups with centers corresponding to homotopy groups of suspensions of Eilenberg-MacLane spaces, a novel connection between algebra and topology.

Findings

Explicit construction of finitely presented groups with prescribed centers

Centers of these groups are isomorphic to specific homotopy groups

Bridges between algebraic group theory and algebraic topology

Abstract

For every finite abelian group $A$ and $n\geq 3$, we construct a finitely presented group defined by explicit generators and relations, such that its center is $\pi_n(\Sigma K(A,1))$.