On involutions and generalized symmetric spaces of dicyclic groups

2013/10/01 by Abigail Bishop, Abigail Claire Bishop, Bishop, Abigail +10
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Geometric and Algebraic Topology #math.GR #msc:20C99 #msc:53C35

paper · pdf · doi:10.48550/arxiv.1310.0121

arxiv created 2013/10/01 · arxiv updated 2013/10/02

Abstract

Let G=\Dc_n be the dicyclic group of order 4n. Let φ be an automorphism of G of order k. We describe φ and the generalized symmetric space Q of G associated with φ. When φ is an involution, we describe its fixed point group H=G^φ along with the H-orbits and G-orbits of Q corresponding to the action of φ-twisted conjugation.

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