Abstract: According to the group chain[SO(5)⊃U(1)_DⓧSU(2)_T]ⓧ[Sp(2j+1)⊃O(3)],the coupling states of j-shell nucleons are classified by D=(n-2 j-1)/2,isospin T,angular momentum J and generalized quasispin[s,t],where s is generalized siniority and t is reduced isospin;the multiplicities classified are products of SO(5)⊃U(1)_DⓧSU(2)_T and Sp(2j+1)⊃O(3) group reduction multiplicities.The explicit formulas for the two group reduction multiplicities are presented,and some results calculated are listed.

Key words: quasispin, isospin, nuclear physics, group theory