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We have used the SmallGroups library of groups, together with the computeralgebra systems GAP and Mathematica, to search for groups with athree-dimensional irreducible representation in which one of the groupgenerators has a twice-degenerate eigenvalue while another generator hasnon-degenerate eigenvalues. By assuming one of these group generators tocommute with the charged-lepton mass matrix and the other one to commute withthe neutrino (Dirac) mass matrix, one derives group-theoretical predictions forthe moduli of the matrix elements of either a row or a column of the leptonmixing matrix. Our search has produced several realistic predictions for eitherthe second row, or the third row, or for any of the columns of that matrix.

Group-theoretical search for rows or columns of the lepton mixing matrix