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An exotic presentation of $Q_{28}$

Wajid H Mannan and Tomasz Popiel

Algebraic & Geometric Topology 21 (2021) 2065–2084
Abstract

We introduce a new family of presentations for the quaternion groups and show that for the quaternion group of order 28, one of these presentations has nonstandard second homotopy group.

Keywords
group presentation, homotopy group, Wall's D(2) problem
Mathematical Subject Classification
Primary: 57K20, 57M05
Secondary: 16S34, 20C05, 20C10, 55N25, 55P15, 55Q91
References
Publication
Received: 1 April 2020
Revised: 22 June 2020
Accepted: 18 September 2020
Published: 18 August 2021
Authors
Wajid H Mannan
School of Mathematical Sciences
Queen Mary University of London
London
United Kingdom
https://www.qmul.ac.uk/maths/profiles/mannanw.html
Tomasz Popiel
Department of Mathematics
The University of Auckland
Auckland
New Zealand