Asphericity and finiteness for certain group presentations

Edjvet, Martin; Eljamel, Noha

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: Jul 12, 2020
• 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
• Contract Date: Jul 9, 2019