On the LS-category of homomorphisms of groups with torsion

Abstract

We prove the equality cat\((\phi)=\)cd\((\phi)\) for homomorphisms \(\phi:\Gamma\to \Lambda\) of any finitely generated abelian group \(\Gamma\). In addition, we prove that the Lusternik-Schnirelmann category and the cohomological dimension of any nonzero homomorphism of a torsion group cannot be finite.