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arXiv · 1303.1656

Groups with infinitely many ends are not fraction groups

Dawid Kielak
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Abstract

We show that any finitely generated group $F$ with infinitely many ends is not a group of fractions of any finitely generated proper subsemigroup $P$, that is $F$ cannot be expressed as a product $P P^{-1}$. In particular this solves a conjecture of Navas in the positive. As a corollary we obtain a new proof of the fact that finitely generated free groups do not admit isolated left-invariant orderings.

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Dawid Kielak. 2013-03-07. Groups with infinitely many ends are not fraction groups. https://doi.org/10.4171/ggd/314

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