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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.

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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