On the Structure of Involutions and Symmetric Spaces of Dihedral Groups

TL;DR

This paper explores the structure of automorphisms, involutions, and symmetric spaces within finite dihedral groups, extending the concept of symmetric spaces to these algebraic structures.

Contribution

It introduces the study of symmetric space analogues for dihedral groups, analyzing automorphisms and involutions in this context.

Findings

Characterized involutions of automorphism groups

Determined fixed groups for each automorphism

Described symmetric spaces associated with dihedral groups

Abstract

We initiate the study of analogues of symmetric spaces for the family of finite dihedral groups. In particular, we investigate the structure of the automorphism group, characterize the involutions of the automorphism group, and determine the fixed-group and symmetric space of each automorphism.