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arXiv · 1801.09241

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

Michael Handel·Lee Mosher
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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.

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Michael Handel, Lee Mosher. 2018-01-28. Virtually abelian subgroups of $IA_n(Z/3)$ are abelian. https://arxiv.org/abs/1801.09241

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