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On soluble groups of automorphisms of nonorientable Klein surfaces

G. Gromadzki (1992)

Fundamenta Mathematicae

We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.

On the Cantor-Bendixson rank of metabelian groups

Yves Cornulier (2011)

Annales de l’institut Fourier

We study the Cantor-Bendixson rank of metabelian and virtually metabelian groups in the space of marked groups, and in particular, we exhibit a sequence ( G n ) of 2-generated, finitely presented, virtually metabelian groups of Cantor-Bendixson rank  ω n .

On the complexity of braids

Ivan Dynnikov, Bert Wiest (2007)

Journal of the European Mathematical Society

We define a measure of “complexity” of a braid which is natural with respect to both an algebraic and a geometric point of view. Algebraically, we modify the standard notion of the length of a braid by introducing generators i j , which are Garside-like half-twists involving strings i through j , and by counting powered generators Δ i j k as log ( | k | + 1 ) instead of simply | k | . The geometrical complexity is some natural measure of the amount of distortion of the n times punctured disk caused by a homeomorphism. Our main...

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