A short note on the topological decomposition of the central product of groups. (English) Zbl 1524.57004
Summary: It has been recently observed that a topological decomposition of the Pauli group, as central product of the quaternion group of order eight and the cyclic group of order four, influences some significant dynamical systems in mathematical physics. The connection between groups of symmetries 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 Riemannian 3-manifold whose fundamental group is epimorphically mapped onto a central product.
MSC:
| 57M07 | Topological methods in group theory |
| 57M60 | Group actions on manifolds and cell complexes in low dimensions |
| 05C15 | Coloring of graphs and hypergraphs |
| 20D60 | Arithmetic and combinatorial problems involving abstract finite groups |
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