All Outputs (6)

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.

Notions of anonymous existence in Martin-Löf type theory (2017)
Journal Article
Kraus, N., Escardo, M., Coquand, T., & Altenkirch, T. (in press). Notions of anonymous existence in Martin-Löf type theory. Logical Methods in Computer Science, 13(1),

As the groupoid model of Hofmann and Streicher proves, identity proofs in intensional Martin-L\"of type theory cannot generally be shown to be unique. Inspired by a theorem by Hedberg, we give some simple characterizations of types that do have uniqu... Read More about Notions of anonymous existence in Martin-Löf type theory.

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.

Precision assembly of complex cellular microenvironments using holographic optical tweezers (2015)
Journal Article
Kirkham, G. R., Britchford, E., Upton, T., Ware, J., Gibson, G., Devaud, Y., …Shakesheff, K. M. (2015). Precision assembly of complex cellular microenvironments using holographic optical tweezers. Scientific Reports, 5, Article 8577. https://doi.org/10.1038/srep08577

The accurate study of cellular microenvironments is limited by the lack of technologies that can manipulate cells in 3D at a sufficiently small length scale. The ability to build and manipulate multicellular microscopic structures will facilitate a m... Read More about Precision assembly of complex cellular microenvironments using holographic optical tweezers.