On the structure of involutions and symmetric spaces of dihedral groups

We initiate the study of analogues of symmetric spaces for finite groups, with the current work focusing on the family of finite dihedral groups. In particular, we investigate the structure of the automorphism group, characterize the involutions within the automorphism group, and determine the fixed-point subgroup and symmetric space of each automorphism.

我们开创了有限群对称空间类似物的研究，当前工作聚焦于有限二面体群族。具体而言，我们研究了自同构群的结构，刻画了自同构群中的对合，并确定了每个自同构的不动点子群与对称空间。