  The electroweak unification group $G\equiv SU(2)_L\times U(1)_e\times
U(1)_\mu\times U(1)_\tau$ in which each fermion multiplet has its own $U(1)$
factor was proposed in 1986 to get the neutrino mass matrix. In this paper, the
gauge group G is restricted to lepton section only, leaving quark multiplets as
in the standard model. In addition to lepton multiplets $L_e$, $L_\mu$ and
$L_\tau$, there are three $SU(2)$singlet right handed neutrinos
$N_{R}^{(i)}$'s. WIth the breaking of G to $SU(2)_L\times U(1)$, the right
handed neutrinos acquire heavy Majorana masses. Three heavy right handed
neutrinos $N_{R}^{(i)}$'s are available to generate a $3\times 3$ non-diagonal
neutrino mass matrix in terms of three Yukawa couplings $h^{(2)}_{1}$,
$h^{(3)}_{2}$, $h^{(1)}_{3}$ of the Higgs scalar doublet to $L_e$, $L_\mu$,
$L_\tau$ with $N_{R}^{(1)}$, $N_{R}^{(2)}$ and $N_{R}^{(3)}$ respectively.
Three Yukawa couplings can be arranged and expressed in terms of masses $m_e$,
$m_\mu$, $m_\tau$ in three different ways to obtain the results of interest for
Case 1: ($\nu_e \rightarrow \nu_\tau$); Case 2: ($\nu_e \rightarrow \nu_\mu$);
Case 3: ($\nu_\mu \rightarrow \nu_\tau$). The results obtained for the three
cases are compared with the experimental data from neutrino oscillations. Cases
1 and 2 are relevant for solar neutrino oscillations whereas Case 3 is relevant
for atmospheric neutrino oscillations.
