A SHORT NOTE ON THE TOPOLOGICAL DECOMPOSITION OF THE CENTRAL PRODUCT OF GROUPS

It has been recently observed that a topological decomposition of the pauli group, ascentral product of the quaternion group of order eight and the cyclic group of order four, inuencessome significant dynamical systems in mathematical physics. the connection between groups ofsymmetries and dynamical systems is in fact well known, but looking specifically at the algebraic and topological decompositions of the pauli group, we find conditions for the existence of a riemannian3-manifold whose fundamental group is epimorphically mapped onto a central product.