Schur rings over infinite dihedral group

Abstract

Schur rings over the infinite dihedral group $\mathcal{Z}⋊{\mathcal{Z}}_2$ are studied according to properties of Schur rings over infinite groups and the classification of Schur rings over infinite cyclic groups. Schur rings over $\mathcal{Z}⋊{\mathcal{Z}}_2$ are classified under the assumption that $\mathcal{Z}$ is an $\mathcal{A}$-subgroup. Those Schur rings are proved to be traditional.

KEYWORDS:

• Schur rings
• traditional Schur rings
• wedge products

2020 AMS CLASSIFICATION:

• 05E30
• 05E15
• 20C05

Disclosure statement

The authors have no conflict of interest to declare that are relevant to this article.

Additional information

Funding

The work of the first author is supported by Natural Science Foundation of China (No. 12371019, No. 12161035).