On the structure of symmetric spaces of semidihedral groups

Schaefer, Jennifer; Schlechtweg, Kathryn

doi:10.2140/involve.2017.10.665

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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

DOI: 10.2140/involve.2017.10.665

Abstract

We investigate the symmetric spaces associated to the family of semidihedral groups of order $2^{n}$ . 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

Vol. 10, No. 4, 2017