The affine and Euclidean normalizers of the subperiodic groups

TL;DR

This paper derives and lists the affine and Euclidean normalizers for various subperiodic groups, including Frieze, rod, and layer groups, considering special metrics for plane group normalizers.

Contribution

It provides a comprehensive derivation and listing of the affine and Euclidean normalizers for subperiodic groups, including special metrics for layer groups.

Findings

Normalizers for Frieze, rod, and layer groups are explicitly derived.

Special metrics for plane group Euclidean normalizers are considered.

The results facilitate understanding of symmetry group structures.

Abstract

The affine and Euclidean normalizers of the subperiodic groups, the Frieze groups, the rod groups, and the layer groups, are derived and listed. For the layer groups, the special metrics used for plane group Euclidean normalizers have been considered.