Lepton family symmetry and possible application to the Koide mass formula

A finite group generated by four Z3 transformations is applied to lepton families in a supersymmetric model, resulting in the charged-lepton masses mi being proportional to vi2, where vi are three vacuum expectation values. This may be relevant in obtaining the Koide formula me+mμ+mτ=(2/3)(me+mμ+mτ)2.