- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:01
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
9
2015
1
Groups with infinitely many ends are not fraction groups
Dawid
Kielak
Universität Bonn, BONN, GERMANY
Groups with infinitely many ends, groups of fractions, isolated orderings
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.
Group theory and generalizations
317
323
10.4171/GGD/314
http://www.ems-ph.org/doi/10.4171/GGD/314