We quote from the 1995 work (p 20, paragraph 2, line 13): "An improper rotation is a binary operation involving consecutive application of the unitary operations of rotation and reflection through a perpendicular plane (C_n^ms_h = s_hC_n^m = S_n^m)." This does not take into account explicitly that the operation does not mean that a symmetry element exists. We quote from the 1982 work, to make this clear (p 554, under the heading Schöenflies Notation): "In the Schöenflies notation, at the very outset, one needs to reckon with two different ways of writing the symbols, namely the boldface (or italic symbols) and the ordinary symbols. These symbols employing the same letter and number mean two entirely different ideas." Further on page 555 under the subheading Spectroscopist's Alternating (Rotatory-Reflection) Axes, we have "Point groups possessing just alternating axes, symbolized as S_n, involve an n-fold counterclockwise rotation of a motif to give an imaginary motif." The word imaginary is crucial in that students should never get any lingering thought that a rotation axis or a mirror plane exists.

Finally, most discussions on symmetry are based upon just the spectroscopist's viewpoint. No attention is paid the well known Hermann–Mauguin concepts of the crystallographic point of view. I was fortunate in that I had exposure to both view points. I urge the readers to study the excellent article by the late J. D. H. Donnay (Acta Crystallogr. 1972, A28, S110 and the references cited therein.).