Asphericity of a length four relative presentation

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 t...

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Main Authors: Bin Ahmad, Abd Ghafur, Al-Mulla, Muna A., Edjvet, Martin
Format: Article
Published: World Scientific 2016
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Online Access:https://eprints.nottingham.ac.uk/32633/
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author Bin Ahmad, Abd Ghafur
Al-Mulla, Muna A.
Edjvet, Martin
author_facet Bin Ahmad, Abd Ghafur
Al-Mulla, Muna A.
Edjvet, Martin
author_sort Bin Ahmad, Abd Ghafur
building Nottingham Research Data Repository
collection Online Access
description 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.
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spelling nottingham-326332020-05-04T17:51:54Z https://eprints.nottingham.ac.uk/32633/ Asphericity of a length four relative presentation Bin Ahmad, Abd Ghafur Al-Mulla, Muna A. Edjvet, Martin 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. World Scientific 2016-05-13 Article PeerReviewed Bin Ahmad, Abd Ghafur, Al-Mulla, Muna A. and Edjvet, Martin (2016) Asphericity of a length four relative presentation. Journal of Algebra and its Applications, 16 (04). p. 1750076. ISSN 1793-6829 relative group presentation; asphericity http://www.worldscientific.com/doi/abs/10.1142/S0219498817500761 doi:10.1142/S0219498817500761 doi:10.1142/S0219498817500761
spellingShingle relative group presentation; asphericity
Bin Ahmad, Abd Ghafur
Al-Mulla, Muna A.
Edjvet, Martin
Asphericity of a length four relative presentation
title Asphericity of a length four relative presentation
title_full Asphericity of a length four relative presentation
title_fullStr Asphericity of a length four relative presentation
title_full_unstemmed Asphericity of a length four relative presentation
title_short Asphericity of a length four relative presentation
title_sort asphericity of a length four relative presentation
topic relative group presentation; asphericity
url https://eprints.nottingham.ac.uk/32633/
https://eprints.nottingham.ac.uk/32633/
https://eprints.nottingham.ac.uk/32633/