Article
Licensed
Unlicensed
Requires Authentication
Random equations in free groups
-
,
Published/Copyright:
November 25, 2011
Abstract
In this paper we study the asymptotic probability that a random equation in a finitely generated free group F is solvable in F. For one-variable equations this probability is zero, but for split equations, i.e., equations of the form v(x1, . . . , xk) = g, g ∈ F, the probability is strictly between zero and one if k ≥ rank(F) ≥ 2. As a consequence the endomorphism problem in F has intermediate asymptotic density, and we obtain the first natural algebraic examples of subsets of intermediate density in free groups of rank larger than two.
Received: 2011-05-12
Published Online: 2011-11-25
Published in Print: 2011-December
© de Gruyter 2011
You are currently not able to access this content.
You are currently not able to access this content.
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
