Growth rate of an endomorphism of a group
-
Kenneth J. Falconer
,
Benjamin Fine
Abstract
Bowen defined the growth rate of an endomorphism of a finitely generated group and related it to the entropy of a map ƒ : M ↦ M on a compact manifold. In this note we study the purely group theoretic aspects of the growth rate of an endomorphism of a finitely generated group. We show that it is finite and bounded by the maximum length of the image of a generator. An equivalent formulation is given that ties the growth rate of an endomorphism to an increasing chain of subgroups. We then consider the relationship between growth rate of an endomorphism on a whole group and the growth rate restricted to a subgroup or considered on a quotient. We use these results to compute the growth rates on direct and semidirect products. We then calculate the growth rate of endomorphisms on several different classes of groups including abelian and nilpotent.
© de Gruyter 2011
Articles in the same Issue
- The Zieschang–McCool method for generating algebraic mapping-class groups
- A new generic digital signature algorithm
- Subgroups of R. Thompson's group F that are isomorphic to F
- Random equations in free groups
- Growth rate of an endomorphism of a group
- On Cayley graphs of virtually free groups
- Quantum algorithms for fixed points and invariant subgroups
- A note on faithful representations of limit groups
Articles in the same Issue
- The Zieschang–McCool method for generating algebraic mapping-class groups
- A new generic digital signature algorithm
- Subgroups of R. Thompson's group F that are isomorphic to F
- Random equations in free groups
- Growth rate of an endomorphism of a group
- On Cayley graphs of virtually free groups
- Quantum algorithms for fixed points and invariant subgroups
- A note on faithful representations of limit groups
