is shown that the reduction of the circular quantum oscillator by the
Z(2) group action results in the two systems: a two-dimensional hydrog
en atom, and a ''charge-charged magnetic vortex'' one, with spin-1/2.
Analogously, the Z(N) reduction of the two-dimensional system with the
central potential r(2(N-1)) results into N bound ''charge-magneticver
tex'' systems with the interaction potential r(2(1/N-1)) and spins sig
ma = k/N, K = 0,1,...,N - 1.