Example of non-abelian partially ordered group

All strictly increasing functions $\mathbb R\to \mathbb R$, equipped with composition as the group operation and with the usual partial order given by $f\leq g$ if and only if $f(x)\leq g(x)$ for every $x\in\mathbb R$. Note that this is a lattice ordered group.

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Order Theory

Abstract Algebra

Group Theory

Examples Counterexamples

Lattice Orders

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