On involutions and generalized symmetric spaces of dicyclic groups

• DOI: 10.48550/arxiv.1310.0121
• Publication Date: 2013-01-01
• Authors: Bishop, Abigail; Cyr, Christopher; Hutchens, John; May, Clover; Schwartz, Nathaniel; Turner, Bethany
• Keywords: 53C35, 20C99,; FOS: Mathematics; Group Theory (math.GR); Mathematics - Group Theory

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