On the structure of involutions and symmetric spaces of dihedral groups. (English) Zbl 1336.20025

Cunningham, K. K. A.; Edgar, Tom; Helminck, A. G.; Jones, B. F.; Oh, H.; Schwell, R.; Vasquez, J. F.

Note Mat. 34, No. 2, 23-40 (2014).

Summary: 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.

MSC:

20D45	Automorphisms of abstract finite groups
20E36	Automorphisms of infinite groups
53C35	Differential geometry of symmetric spaces

Keywords:

finite dihedral groups; generalized symmetric spaces; involutions; automorphisms; numbers of conjugacy classes; fixed points

Software:

OEIS