Involve: A Journal of Mathematics

  • Involve
  • Volume 12, Number 4 (2019), 565-583.

The classification of involutions and symmetric spaces of modular groups

Marc Besson and Jennifer Schaefer

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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.

Article information

Source
Involve, Volume 12, Number 4 (2019), 565-583.

Dates
Received: 6 July 2017
Revised: 21 August 2018
Accepted: 30 October 2018
First available in Project Euclid: 30 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.involve/1559181653

Digital Object Identifier
doi:10.2140/involve.2019.12.565

Mathematical Reviews number (MathSciNet)
MR3941599

Zentralblatt MATH identifier
07072540

Subjects
Primary: 20D15: Nilpotent groups, $p$-groups 53C35: Symmetric spaces [See also 32M15, 57T15]

Keywords
modular 2-group symmetric spaces automorphisms involutions

Citation

Besson, Marc; Schaefer, Jennifer. The classification of involutions and symmetric spaces of modular groups. Involve 12 (2019), no. 4, 565--583. doi:10.2140/involve.2019.12.565. https://projecteuclid.org/euclid.involve/1559181653


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