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Asphericity of a length four relative presentation

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


Abd Ghafur Bin Ahmad

Muna A. Al-Mulla


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.


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),

Journal Article Type Article
Acceptance Date Apr 4, 2016
Publication Date May 13, 2016
Deposit Date Apr 5, 2016
Publicly Available Date May 14, 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
Keywords relative group presentation; asphericity
Public URL
Publisher URL
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,


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