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We describe unicorn paths in the arc graph and show that they form 1-slim triangles and are invariant under taking subpaths. We deduce that all arc graphs are 7-hyperbolic. Considering the same paths in the arc and curve graph, this also shows that all curve graphs are 17-hyperbolic, including closed surfaces.

(2,3)-generation of the groups PSL6(q)

Tabakov, K., Tchakerian, K. (2011)

Serdica Mathematical Journal

2010 Mathematics Subject Classification: 20F05, 20D06.We prove that the group PSL6(q) is (2,3)-generated for any q. In fact, we provide explicit generators x and y of orders 2 and 3, respectively, for the group SL6(q).

6-BFC groups

Cliff David, James Wiegold (2006)

Rendiconti del Seminario Matematico della Università di Padova

(Cyclic) subgroup separability of HNN and split extensions

Firat Ateş, A. Sinan Çevik (2007)

Mathematica Slovaca

[unknown]

О.Г. Харлампович (1987)

Algebra i Logika

[unknown]

Nariya Kawazumi, Yusuke Kuno (0)

Annales de l’institut Fourier

[unknown]

Pierre-Emmanuel Caprace, David Hume (0)

Annales de l’institut Fourier

[unknown]

Marc Bourdon (0)

Annales de l’institut Fourier

$Σ$ -chamber systems, coloured graphs and orbifolds.

Balke, Ludwig, Valverde, Alba (1996)

Beiträge zur Algebra und Geometrie

$σ$ -interpolation lattice-ordered groups

Michael R. Darnel (2000)

Czechoslovak Mathematical Journal

In [1], Jakubík showed that the class of $σ$ -interpolation lattice-ordered groups forms a radical class, but left open the question of whether the class forms a torsion class. In this paper, we show that this class does indeed form a torsion class.

Абстрактные изоморфизмы квазиминимальных групп

К.Н. Пономарëв, K. N. Ponomarëv, K. N. Ponomarëv, K. N. Ponomarëv (1996)

Algebra i Logika

Автоморфизмы матричных групп над коммутативными кольцами

В.М. Петечук (1982)

Matematiceskij sbornik

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