International
Tables for Crystallography Volume A Spacegroup symmetry Edited by M. I. Aroyo © International Union of Crystallography 2016 
International Tables for Crystallography (2016). Vol. A, ch. 1.2, pp. 1921

In the 1970s, when the International Union of Crystallography (IUCr) planned a new series of International Tables for Crystallography to replace the series International Tables for Xray Crystallography (1952), there was some confusion about the use of the term symmetry element. Crystallographers and mineralogists had used this term for rotation and rotoinversion axes and reflection planes, in particular for the description of the morphology of crystals, for a long time, although there had been no strict definition of `symmetry element'. With the impact of mathematical group theory in crystallography the term element was introduced with another meaning, in which an element is a member of a set, in particular as a group element of a group. In crystallography these group elements, however, were the symmetry operations of the symmetry groups, not the crystallographic symmetry elements. Therefore, the IUCr Commission on Crystallographic Nomenclature appointed an Adhoc Committee on the Nomenclature of Symmetry with P. M. de Wolff as Chairman to propose definitions for terms of crystallographic symmetry and for several classifications of crystallographic space groups and point groups.
In the reports of the Adhoc Committee, de Wolff et al. (1989) and (1992) with Addenda, Flack et al. (2000), the results were published. To define the term symmetry element for any symmetry operation was more complicated than had been envisaged previously, in particular for unusual screw and glide components.
According to the proposals of the Committee the following procedure has been adopted (cf. also Table 1.2.3.1):

Examples
References
International Tables for Xray Crystallography (1952). Vol. I, edited by N. F. M. Henry & K. Lonsdale. Birmingham: Kynoch Press.Flack, H. D., Wondratschek, H., Hahn, Th. & Abrahams, S. C. (2000). Symmetry elements in space groups and point groups. Addenda to two IUCr Reports on the Nomenclature of Symmetry. Acta Cryst. A56, 96–98.
Wolff, P. M. de, Billiet, Y., Donnay, J. D. H., Fischer, W., Galiulin, R. B., Glazer, A. M., Senechal, M., Shoemaker, D. P., Wondratschek, H., Hahn, Th., Wilson, A. J. C. & Abrahams, S. C. (1989). Definition of symmetry elements in space groups and point groups. Report of the International Union of Crystallography AdHoc Committee on the Nomenclature of Symmetry. Acta Cryst. A45, 494–499.
Wolff, P. M. de, Billiet, Y., Donnay, J. D. H., Fischer, W., Galiulin, R. B., Glazer, A. M., Hahn, Th., Senechal, M., Shoemaker, D. P., Wondratschek, H., Wilson, A. J. C. & Abrahams, S. C. (1992). Symbols for symmetry elements and symmetry operations. Final Report of the International Union of Crystallography AdHoc Committee on the Nomenclature of Symmetry. Acta Cryst. A48, 727–732.