Journal of Generalized Lie Theory and Applications

In this study, we give constructions of right cheban loops of order 4t, using a multiplication defined on cartesian product of (C_2t X C₂) where C_2t is a cyclic group of order 2t, t is a positive integer: 3,4 and 6 and C₂ is a cyclic group of order 2, each gives a right cheban loop of orders 12, 16 and 24. It was found that smallest non-associative right cheban loop is of order 12 and finite examples of right cheban loops of orders 12,16 and 24 are generated as shown in the cayley tables.

This paper aims at studying a new integrable Hamiltonian system due to valent. This is a Hamiltonian system with two degrees of freedom where the additional integral is polynomial of degree 3. The critical points and the bifurcation diagram of the Hamiltonian are obtained and the non-degeneracy conditions are verified. Thereafter the topology of iso-energy surfaces is found. Also for zero value of one of the parameters, the type of non-degenerate critical points of rank zero is calculated, the bifurcation diagram of the momentum map is constructed and finally the molecules (fomenko invariants) are found.