Virtually abelian subgroups of $IA_n(Z/3)$ are abelian

Michael Handel; Lee Mosher

Virtually abelian subgroups of $IA_n(Z/3)$ are abelian

Group Theory 2018-01-30 v1

Authors: Michael Handel , Lee Mosher

Abstract

When studying subgroups of $Out(F_n)$ , one often replaces a given subgroup $H$ with one of its finite index subgroups $H_0$ so that virtual properties of $H$ become actual properties of $H_0$ . In many cases, the finite index subgroup is $H_0 = H \cap IA_n(Z/3)$ . For which properties is this a good choice? Our main theorem states that being abelian is such a property. Namely, every virtually abelian subgroup of $IA_n(Z/3)$ is abelian.

Keywords

virtually abelian groups ia automorphism groups outer automorphism groups finite index subgroups

Cite

@article{arxiv.1801.09241,
  title  = {Virtually abelian subgroups of $IA_n(Z/3)$ are abelian},
  author = {Michael Handel and Lee Mosher},
  journal= {arXiv preprint arXiv:1801.09241},
  year   = {2018}
}

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