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Asphericity and finiteness for certain group presentations

Edjvet, Martin; Eljamel, Noha

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).

Journal Article Type Article
Publication Date Oct 15, 2019
Print ISSN 0021-8693
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 536
Pages 39-81
APA6 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
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
Publisher URL https://www.sciencedirect.com/science/article/pii/S0021869319303667

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