line repetition groups

https://doi.org/10.1351/goldbook.L03564
The possible symmetries of arrays extending in one direction with a fixed @I00954@. @L03556@ chains in the crystalline state must belong to one of the line repetition groups. Permitted symmetry elements are: the identity operation (symbol l); the translation along the chain axis (symbol t); the mirror plane orthogonal to the chain axis (symbol \(m\)) and that containing the chain axis (symbol \(d\)); the glide plane containing the chain axis (symbol \(c\)); the @I03146@ centre, placed on the chain axis (symbol \(i\)); the two-fold axis orthogonal to the chain axis (symbol 2); the helical, or screw, symmetry where the axis of the @H02769@ coincides with the chain axis. In the latter case, the symbol is \(\text{s}\left(A*M/N\right)\), where \(\text{s}\) stands for the screw axis, \(A\) is the class of the @H02769@, * and / are separators, and \(M\) is the integral number of residues contained in \(N\) turns, corresponding to the identity period (\(M\) and \(N\) must be prime to each other). The class index \(A\) may be dropped if deemed unnecessary, so that the @H02769@ may also be simply denoted as \(\text{s}\left(M/N\right)\).
Source:
Purple Book, 1st ed., p. 79 [Terms]