#### 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 ${2}^{m}$ 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.

##### Keywords
modular 2-group, symmetric spaces, automorphisms, involutions
##### Mathematical Subject Classification 2010
Primary: 20D15, 53C35