Vol. 12, No. 4, 2019

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The classification of involutions and symmetric spaces of modular groups

Marc Besson and Jennifer Schaefer

Vol. 12 (2019), No. 4, 565–583
DOI: 10.2140/involve.2019.12.565
Abstract

The involutions and the symmetric spaces associated to the family of modular groups of order 2m are explored. We begin by analyzing the structure of the automorphism group and by establishing which automorphisms are involutions. We conclude by calculating the fixed-point group and symmetric spaces determined by each involution.

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Keywords
modular 2-group, symmetric spaces, automorphisms, involutions
Mathematical Subject Classification 2010
Primary: 20D15, 53C35
Milestones
Received: 6 July 2017
Revised: 21 August 2018
Accepted: 30 October 2018
Published: 16 April 2019

Communicated by Kenneth S. Berenhaut
Authors
Marc Besson
Mathematics Department
University of North Carolina at Chapel Hill
Chapel Hill, NC
United States
Jennifer Schaefer
Department of Mathematics and Computer Science
Dickinson College
Carlisle, PA
United States