Central extensions of gyrocommutative gyrogroups \linebreak (K-loops) are studied in order to clarify the status of a cocycle equation introduced by Smith and Ungar. A sufficient and necessary conditions under which a central invariant extension is a gyrocommutative gyrogroup are formulated in terms of a 2-cochain $f(x,y).$ In particular, it is shown that for central invariant extensions of gyrocommutative gyrogroups defined by Cartan decompositions of simple Lie algebras, the corresponding $f(x,y)$ satisfies the cocycle equation, provided an extension is a gyrocommutative gyrogroup.