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All Outputs (6)

Asphericity and finiteness for certain group presentations (2019)
Journal Article
Edjvet, M., & Eljamel, N. (2019). Asphericity and finiteness for certain group presentations. Journal of Algebra, 536, 39-81. https://doi.org/10.1016/j.jalgebra.2019.06.028

We study diagrammatic reducibility for the relative group presentations Rn(k, l, ε) = H, x | t 3 x k t 2 x ε(k+l) where H = t | t n , n ≥ 7, k ≥ 1, l ≥ 0 and ε = ±1. We apply our results to classify finiteness for the group Gn(k, l, ε) defined by Rn(... Read More about Asphericity and finiteness for certain group presentations.

Asphericity of positive free product length 4 relative group presentations (2018)
Journal Article
Aldwaik, S., Edjvet, M., & Juhasz, A. (2019). Asphericity of positive free product length 4 relative group presentations. Forum Mathematicum, 31(1), 49-68. https://doi.org/10.1515/forum-2017-0141

© 2018 Walter de Gruyter GmbH, Berlin/Boston. Excluding some exceptional cases, we determine the asphericity of the relative presentation P = ,where a, b ∈ G \ {1} and 1 ≤ m ≤ n. If H = ≤ G, the exceptional cases occurwhen a = b2 or when H is isomor... Read More about Asphericity of positive free product length 4 relative group presentations.

Solving equations of length seven over torsion-free groups (2017)
Journal Article
Bibi, M., & Edjvet, M. (in press). Solving equations of length seven over torsion-free groups. Journal of Group Theory, 21(1), https://doi.org/10.1515/jgth-2017-0032

Prishchepov [16] proved that all equations of length at most six over torsion-free groups are solvable. A different proof was given by Ivanov and Klyachko in [12]. This supports the conjecture stated by Levin [15] that any equation over a torsion-fre... Read More about Solving equations of length seven over torsion-free groups.

The infinite Fibonacci groups and relative asphericity (2017)
Journal Article
Edjvet, M., & Juhasz, A. (2017). The infinite Fibonacci groups and relative asphericity. Transactions of the London Mathematical Society, 4(1), https://doi.org/10.1112/tlm3.12007

We prove that the generalised Fibonacci group F (r, n) is infinite for (r, n) ? {(7 + 5k, 5), (8 + 5k, 5) : k ? 0}. This together with previously known results yields a complete classification of the finite F (r, n), a problem that has its origins in... Read More about The infinite Fibonacci groups and relative asphericity.

On the asphericity of a family of positive relative group presentations (2017)
Journal Article
Aldwaik, S., & Edjvet, M. (in press). On the asphericity of a family of positive relative group presentations. Proceedings of the Edinburgh Mathematical Society, https://doi.org/10.1017/S0013091516000419

Excluding four exceptional cases, the asphericity of the relative presentation P= ?G; x|xmgxh? for m ? 2 is determined. If H = ?g; h? ? G, then the exceptional cases occur when H is isomorphic to C5 or C6.

Asphericity of a length four relative presentation (2016)
Journal Article
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

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}... Read More about Asphericity of a length four relative presentation.