#### 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 ${2}^{n}$. 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