11,446 research outputs found
c-Regular cyclically ordered groups
We define and we characterize regular and c-regular cyclically ordered
abelian groups. We prove that every dense c-regular cyclically ordered abelian
group is elementarily equivalent to some cyclically ordered group of unimodular
complex numbers, that every discrete c-regular cyclically ordered abelian group
is elementarily equivalent to some ultraproduct of finite cyclic groups, and
that the discrete regular non-c-regular cyclically ordered abelian groups are
elementarily equivalent to the linearly cyclically ordered group of integers.Comment: 20 page
Infinite words and universal free actions
This is the second paper in a series of three, where we take on the unified
theory of non-Archimedean group actions, length functions and infinite words.
Here, for an arbitrary group of infinite words over an ordered abelian
group we construct a -tree equipped with a free
action of . Moreover, we show that is a universal tree for in
the sense that it isometrically embeds in every -tree equipped with a
free -action compatible with the original length function on .Comment: 20 pages, 4 figure
-free groups are CAT(0)
We show that every group with free -length function is CAT(0).Comment: To be published in the Journal of the London Mathematical Society.
This version is very close to the accepted version. The exposition greatly
improved due to the referee's comment
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