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All non-equivalent solutions of vacuum Maxwell equations are found for thecase when space-time manifolds admit simply transitive four-parameter groups ofmotions $G_4(N)$. The potentials of the admissible electromagnetic fields admitthe existence of the algebra of motion integrals of the Hamilton-Jacobi andKlein-Gordon-Fock equations which is isomorphic to the algebra of the groupoperators for the same group $G_4(N)$

Solutions of Maxwell equations for admissible electromagnetic fields, in spaces with simply transitive four-parameter groups of motions