Asphericity of a length four relative presentationTools Bin Ahmad, Abd Ghafur and AlMulla, Muna A. and Edjvet, Martin Asphericity of a length four relative presentation. Journal of Algebra and its Applications . ISSN 17936829 (In Press)
AbstractWe 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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