Infinitely many symmetries and symmetry reduction of (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

Integrability condition of （2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation are obtained by Painléve-test. Based on this condition and Painléve-test, the bilinear form of GCBS equation is found. Towards this bilinear form infinitely many formal series symmetries are found by the formal series symmetry method, the obtained symmetries are used to get the symmetry reductions of GCBS equation.