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Questions about the branch of algebra that deals with groups.
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Subgroup of lattice-ordered group
Let $H$ be a subgroup of a lattice-ordered group $G$. Suppose that $H$ with the induced order is a lattice (but a priori not a sublattice), so that $H$ is a lattice-ordered group too. For $a, b\in H$, …
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367
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Lattice-ordered group of rational rank 1
Does there exist a lattice-ordered, not totally ordered, group of rational rank $1$?
Rational rank 1 means isomorphic to a nonzero subgroup of $\mathbb{Q}$. There exist totally ordered groups of …
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2
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Direct limit of lattice-ordered groups
In general, any abelian group can be expressed as a direct limit of its f.g. subgroups. For the case of $\ell$-group (lattice-ordered group) is that true or not? As an abelian group we do not have pro …
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Spliting of short exact exact sequences of partially ordered groups
Consider a short exact sequence of partially ordered groups
$$0 \longrightarrow H \stackrel{\alpha}{\longrightarrow} G \stackrel{\beta} {\longrightarrow} G/H \longrightarrow 0 ,$$ where $H$ is a conve …