Asphericity of a length four relative presentation

Bin Ahmad, Abd Ghafur; Al-Mulla, Muna A.; Edjvet, Martin

Abstract

We consider the relative group presentation P = < G, X | R > where X = { x \} and R = { xg_1 xg_2 xg_3 x^{-1} g_4 }. We show modulo a small number of exceptional cases exactly when P is aspherical. If the subgroup H of G is given by H = < g_1^{-1} g_2, g_1^{-1} g_3 g_1 , g_4 > then the exceptional cases occur when H is isomorphic to one of C_5,C_6,C_8 or C_2 X C_4.

Citation

Bin Ahmad, A. G., Al-Mulla, M. A., & Edjvet, M. (2016). Asphericity of a length four relative presentation. Journal of Algebra and Its Applications, 16(4), https://doi.org/10.1142/S0219498817500761

• Journal Article Type: Article
• Acceptance Date: Apr 4, 2016
• Publication Date: May 13, 2016
• Deposit Date: Apr 5, 2016
• Publicly Available Date: Nov 23, 2017
• Journal: Journal of Algebra and its Applications
• Print ISSN: 0219-4988
• Electronic ISSN: 1793-6829
• Publisher: World Scientific
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Issue: 4
• DOI: https://doi.org/10.1142/S0219498817500761
• Keywords: relative group presentation; asphericity
• Public URL: https://nottingham-repository.worktribe.com/output/790046
• Publisher URL: http://www.worldscientific.com/doi/abs/10.1142/S0219498817500761
• Additional Information: Electronic version of an article published as Journal of Algebra and its Applications, 16, 04, 2016, 1750076 (27 p.), doi:10.1142/S0219498817500761 © World Scientific Publishing Company, http://www.worldscientific.com/worldscinet/jaa