  All external electromagnetic fields in which the Klein-Gordon-Fock equation
admits the first-order symmetry operators are found, provided that in the
space-time $V_4$ a group of motion $G_3$ acts simply transitively on a non-null
subspace of transitivity $V_3$. It is shown that in the case of a Riemannian
space $V_n$, in which the group $G_r$ acts simply transitively, the algebra of
symmetry operators of the $n$-dimensional Klein-Gordon-Fock equation in an
external admissible electromagnetic field coincides with the algebra of
operators of the group $G_r$.
