A Note on Embedding Nonabelian Finite Flavor Groups in Continuous Groups

Abstract

A nonabelian finite flavor group $G\subset SO(3)$ can have double covering $G^{{}^{\prime }}\subset SU(2)$ such that $G\not\subset G^{{}^{\prime }}$. This situation is not contradictory, but quite natural, and we give explicit examples such as $G=D_n,G^{{}^{\prime }}=Q_{2n}$ and $G=T,G^{{}^{\prime }}=T^{{}^{\prime }}$. This observation can be crucial in particle theory model building.

Comments: Example of application added