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Asphericity of a length four relative presentation

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

Authors

Abd Ghafur Bin Ahmad ghafur@ukm.my

Muna A. Al-Mulla malmulla@fku.edu.sa

Martin Edjvet martin.edjvet@nottingham.ac.uk



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.

Journal Article Type Article
Publication Date May 13, 2016
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
APA6 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), doi:10.1142/S0219498817500761
DOI https://doi.org/10.1142/S0219498817500761
Keywords relative group presentation; asphericity
Publisher URL http://www.worldscientific.com/doi/abs/10.1142/S0219498817500761
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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