An exotic presentation of Q28

Mannan, Wajid H; Popiel, Tomasz

doi:10.2140/agt.2021.21.2065

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An exotic presentation of $Q_{28}$

Wajid H Mannan and Tomasz Popiel

Algebraic & Geometric Topology 21 (2021) 2065–2084

DOI: 10.2140/agt.2021.21.2065

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

Volume 21, issue 4 (2021)