All Outputs (4)

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.