4 citations · 7 across the 3 of their papers we have counts for
6 papers · 1 filter
Nonvanishing of algebraic entropy for geometrically finite groups of isometries of Hadamard manifolds
Roger C. Alperin, Guennady A. Noskov
We prove that any geometrically finite (nonelementary) group of isometries of a pinched Hadamard manifold has uniform exponential growth.
Separability of Solvable Subgroups in Linear Groups
Roger Alperin, Benson Farb
Let G be a finitely generated linear group over a field of characteristic 0. Suppose that every solvable subgroup of G is polycyclic. Then the claim is made that any solvable subgr…
Uniform Growth, Actions on Trees and
Roger C. Alperin, Guennadi A. Noskov
We use actions on trees to determine uniform exponential growth for subgroups of .
A strong Schottky Lemma for nonpositively curved singular spaces
Roger C. Alperin, Benson Farb, Guennadi A. Noskov
In this paper we give a criterion for pairs of isometries of a nonpositively curved metric space to generate a free group. This criterion holds only in singular spaces, for example…
Uniform Exponential Growth of Polycyclic Groups
Roger C. Alperin
We prove that polycyclic groups are of polynomial growth or of uniform exponential growth.
Solvable Groups of Exponential Growth and HNN Extensions
Roger Alperin
We prove the following version of Milnor's theorem on solvable groups of exponential growth: A finitely generated solvable group which is not polycyclic contains an ascending HNN e…