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Groups with infinitely many ends are not fraction groups
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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.
European Mathematical Society - EMS - Publishing House GmbH
Title: Groups with infinitely many ends are not fraction groups
Description:
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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