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Groups generated by two mutually Engel periodic elements

H. Heineken (2000)

Bollettino dell'Unione Matematica Italiana

Scriviamo [ x , y ] = [ x , 1 y ] ed [ [ x , k y ] , y ] = [ x , k + 1 y ] . Cerchiamo gruppi S ⁢ L ⁢ 2 , q con generatori x , y tali che [ x , m y ] = x ed [ y , n x ] = y per alcuni numeri naturali m , n .

Groups of given intermediate word growth

Laurent Bartholdi, Anna Erschler (2014)

Annales de l’institut Fourier

We show that there exists a finitely generated group of growth ∼ f for all functions f : ℝ + → ℝ + satisfying f ( 2 R ) ≤ f ( R ) 2 ≤ f ( η + R ) for all R large enough and η + ≈ 2 . 4675 the positive root of X 3 - X 2 - 2 X - 4 . Set α - = log 2 / log η + ≈ 0 . 7674 ; then all functions that grow uniformly faster than exp ( R α - ) are realizable as the growth of a group.We also give a family of sum-contracting branched groups of growth ∼ exp ( R α ) for a dense set of α ∈ [ α - , 1 ] .

Groups of real analytic diffeomorphisms of the circle with a finite image under the rotation number function

Yoshifumi Matsuda (2009)

Annales de l’institut Fourier

We consider groups of orientation-preserving real analytic diffeomorphisms of the circle which have a finite image under the rotation number function. We show that if such a group is nondiscrete with respect to the C 1 -topology then it has a finite orbit. As a corollary, we show that if such a group has no finite orbit then each of its subgroups contains either a cyclic subgroup of finite index or a nonabelian free subgroup.

Groups satisfying the maximal condition on subnormal non-normal subgroups

Fausto De Mari, Francesco de Giovanni (2005)

Colloquium Mathematicae

The structure of (generalized) soluble groups for which the set of all subnormal non-normal subgroups satisfies the maximal condition is described, taking as a model the known theory of groups in which normality is a transitive relation.

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