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On the structure of involutions and symmetric spaces of dihedral groups


Abstract


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.

DOI Code: 10.1285/i15900932v34n2p23

Keywords: dihedral groups; symmetric spaces; involutions; automorphisms

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