Vol. 10, No. 4, 2017

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On the structure of symmetric spaces of semidihedral groups

Jennifer Schaefer and Kathryn Schlechtweg

Vol. 10 (2017), No. 4, 665–676
Abstract

We investigate the symmetric spaces associated to the family of semidihedral groups of order 2n . We begin this study by analyzing the structure of the automorphism group and by determining which automorphims are involutions. We then determine the symmetric spaces corresponding to each involution and the orbits of the fixed-point groups on these spaces.

Keywords
semidihedral group, quasidihedral group, symmetric spaces, automorphisms, involutions
Mathematical Subject Classification 2010
Primary: 20D15, 53C35
Milestones
Received: 3 February 2016
Revised: 20 April 2016
Accepted: 12 May 2016
Published: 7 March 2017

Communicated by Scott T. Chapman
Authors
Jennifer Schaefer
Department of Mathematics and Computer Science
Dickinson College
Carlisle, PA 17013
United States
Kathryn Schlechtweg
Columbia University
New York, NY 10027
United States