An Algebraic Classification of Some Solvable Groups of Homeomorphisms
ثبت نشده
چکیده
We produce two separate algebraic descriptions of the isomorphism classes of the solvable subgroups of the group PLo(I) of piecewise-linear orientation-preserving homeomorphisms of the unit interval under the operation of composition, and also of the generalized R. Thompson groups Fn. The first description is as a set of isomorphism classes of groups which is closed under three algebraic operations, and the second is as the set of isomorphism classes of subgroups of a countable collection of easily described groups. We show the two descriptions are equivalent.
منابع مشابه
An Algebraic Classification of Some Solvable Groups of Homeomorphisms
We produce two separate algebraic descriptions of the isomorphism classes of the solvable subgroups of the group PLo(I) of piecewise-linear orientation-preserving homeomorphisms of the unit interval under the operation of composition, and also of the generalized R. Thompson groups Fn. The first description is as a set of isomorphism classes of groups which is closed under three algebraic operat...
متن کاملA Geometric Classification of Some Solvable Groups of Homeomorphisms
We investigate subgroups of the group PLo(I) of piecewise-linear, orientation-preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of generalized Thompson groups Fn. We find geometric criteria determining the derived length of any such group, and use this criteria to produce a geometric classification of the so...
متن کاملA Geometric Classification of Some Solvable Groups of Homeomorphisms
We investigate subgroups of the group PLo(I) of piecewise-linear, orientation-preserving homeomorphisms of the unit interval with finitely many breaks in slope, under the operation of composition, and also subgroups of generalized Thompson groups Fn. We find geometric criteria determining the derived length of any such group, and use this criteria to produce a geometric classification of the so...
متن کاملClassification of solvable groups with a given property
In this paper we classify all finite solvable groups satisfying the following property P5: their orders of representatives are set-wise relatively prime for any 5 distinct non-central conjugacy classes.
متن کاملStructure Theorems for Groups of Homeomorphisms of the Circle
In this partly expository paper, we study the set A of groups of orientation-preserving homeomorphisms of the circle S which do not admit non-abelian free subgroups. We use classical results about homeomorphisms of the circle and elementary dynamical methods to derive various new and old results about the groups in A. Of the known results, we include some results from a family of results of Bek...
متن کامل