Sieve methods in group theory \Rmnum{3}: $\aut(F_n)$

Alexander Lubotzky; Chen Meiri

Sieve methods in group theory \Rmnum{3}: $\aut(F_n)$

Group Theory 2011-06-24 v1

Authors: Alexander Lubotzky , Chen Meiri

Abstract

Let $\pi:\aut(F_n)\rightarrow \aut(\Z^n)$ be the epimorphism induced by the isomorphism $\Z^n \cong F_n/F_n'$ and define $\mathcal{T}_n:=\ker\pi$ . We prove that the subset of $\mathcal{T}_n$ consists of all non-iwip and all non-hyperbolic elements is exponentially small.

Keywords

sieve methods group theory automorphism group free group non-iwip elements non-hyperbolic elements

Cite

@article{arxiv.1106.4637,
  title  = {Sieve methods in group theory \Rmnum{3}: $\aut(F_n)$},
  author = {Alexander Lubotzky and Chen Meiri},
  journal= {arXiv preprint arXiv:1106.4637},
  year   = {2011}
}

Comments

8 pages

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