## Residual (torsion-free nilpotence) in one-relator groups

#### Andrew Glass (Cambridge)

Theorem: Let $$G$$ be an extension of a residually (torsion-free nilpotent) group $$K$$ by a bi-orderable abelian group $$\Phi$$.
Suppose that the real vector space $$V=K^{\rm ab}\otimes \mathbb{R}$$ is finite-dimensional, and that all eigenvalues of maps induced on $$V$$ by elements of $$\Phi$$ are positive real numbers. Then $$G$$ is bi-orderable.