Questions tagged [ordered-groups]

Groups (possibly semigroups) endowed with possibly left/right/bi-invariant partial/total orderings. Study of such orders on groups.

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Continuous real action on affine functions over a Choquet simplex

Let $K$ be a metrizable Choquet simplex. We define $A=\operatorname{Aff}(K,\mathbb{R})$ as the set of real-valued affine continuous functions. This has both the structure of a real Banach space as ...
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Topology of the Malcev-Neumann group ring

For a ring $R$ and a group $G$ the group ring $R[G]$ consist of maps from $G$ to $R$ with finite support. It was shown that if the group is fully ordered them this ring can be embedded in a division ...
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Least positive elements of discrete preorders on surface groups

A left-invariant preordering on a group $G$ is a reflexive, transitive and a complete relation $\preceq$ on $G$ such that $x\preceq y$ implies $gx\prec gy$ for any $g$ (anticommutativity is not ...
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What will be the smallest value of $k$ such that $P(k)=m$?

Let us suppose that we have a group of order $p^k$, where $p$ is prime.In General,there is one group group of order $p^k$ for each set of positive integers whose sum is $k$(such a set is called ...
• 113
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Interleaving in Viennot's Heaps models?

I am looking for past results on interleaving of heaps (in the sense of Viennot). For a very simplified example, suppose I have two pieces, (b1 a1 b1), and (b2 c2 b2), where the letter represents a ...
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Partial orders on $\mathbb{N}^m$ compatible with addition

I'm looking for a classification (or just non-trivial examples) of partial orders on monoid $\mathbb{N}^{m}$ that are compatible with addition. That is, partial orders $\leq$ satisfying two additional ...
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An equivariant Hahn embedding theorem?

The Hahn Embedding Theorem asserts that for any (linearly) ordered abelian group $\Lambda$, there exists a linearly ordered indexing set $\Omega$ such that $\Lambda$ admits an order-preserving group ...
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Do all right orderable groups have the Haagerup property?

Do all right orderable groups have the Haagerup property? Recall that a group is right orderable if there exists a total order $\leq$ on it such that $a\leq b\Rightarrow ac\leq bc$. This property is ...
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