On involutions and generalized symmetric spaces of dicyclic groups

Abigail Bishop; Christopher Cyr; John Hutchens; Clover May; Nathaniel Schwartz; Bethany Turner

On involutions and generalized symmetric spaces of dicyclic groups

Group Theory 2013-10-02 v1

Authors: Abigail Bishop , Christopher Cyr , John Hutchens , Clover May , Nathaniel Schwartz , Bethany Turner

Abstract

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

Keywords

dicyclic groups involutions generalized symmetric spaces automorphisms fixed point groups twisted conjugation group orbits

Cite

@article{arxiv.1310.0121,
  title  = {On involutions and generalized symmetric spaces of dicyclic groups},
  author = {Abigail Bishop and Christopher Cyr and John Hutchens and Clover May and Nathaniel Schwartz and Bethany Turner},
  journal= {arXiv preprint arXiv:1310.0121},
  year   = {2013}
}

On involutions and generalized symmetric spaces of dicyclic groups

Abstract

Keywords

Cite

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