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Asphericity and finiteness for certain group presentations

Edjvet, Martin; Eljamel, Noha

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Authors

Martin Edjvet

Noha Eljamel



Abstract

We study diagrammatic reducibility for the relative group presentations Rn(k, l, ε) = H, x | t 3 x k t 2 x ε(k+l) where H = t | t n , n ≥ 7, k ≥ 1, l ≥ 0 and ε = ±1. We apply our results to classify finiteness for the group Gn(k, l, ε) defined by Rn(k, l, ε) apart from the two exceptional cases (n, k, l, ε) = (7,2,1,-1) and (9,1,1,-1).

Citation

Edjvet, M., & Eljamel, N. (2019). Asphericity and finiteness for certain group presentations. Journal of Algebra, 536, 39-81. https://doi.org/10.1016/j.jalgebra.2019.06.028

Journal Article Type Article
Acceptance Date Jun 28, 2019
Online Publication Date Jul 11, 2019
Publication Date Oct 15, 2019
Deposit Date Jul 9, 2019
Publicly Available Date Mar 28, 2024
Journal Journal of Algebra
Print ISSN 0021-8693
Electronic ISSN 1090-266X
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 536
Pages 39-81
DOI https://doi.org/10.1016/j.jalgebra.2019.06.028
Keywords ashericity; relative group presentation; picture; relative diagram; curvature; diagrammatically reducible 2010 Mathematics subject classification: 20F05; 57M05
Public URL https://nottingham-repository.worktribe.com/output/2291531
Publisher URL https://www.sciencedirect.com/science/article/pii/S0021869319303667

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