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Ordered groups and ordered geometries
Journal of Geometry, 2014The authors study the relationship between ordered geometries and ordered groups. They show that a singular metric plane in the sense of \textit{F. Bachmann} [Ebene Spiegelungsgeometrie. Eine Vorlesung über Hjelmslev-Gruppen. Mannheim etc.: BI-Wissenschaftsverlag (1989; Zbl 0681.51001)] can be ordered if and only if the translation group admits an ...
Struve, Rolf, Struve, Horst
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Algebra and Logic, 2003
\textit{P. Dehornoy} [J. Knot Theory Ramifications 4, No. 1, 33-79 (1995; Zbl 0873.20030)] has proved that the braid group \(B(n)\) possesses a right linear order, i.e., a right linear order such that \(x\leq y\) implies \(xz\leq yz\) for any \(x,y,z\in B(n)\).
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\textit{P. Dehornoy} [J. Knot Theory Ramifications 4, No. 1, 33-79 (1995; Zbl 0873.20030)] has proved that the braid group \(B(n)\) possesses a right linear order, i.e., a right linear order such that \(x\leq y\) implies \(xz\leq yz\) for any \(x,y,z\in B(n)\).
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Right-Ordered Polycyclic Groups
Canadian Mathematical Bulletin, 1974One of the features that make right-ordered groups harder to investigate than ordered groups is that their system of convex subgroups may fail to have the following property:(*) if C and C’ are convex subgroups of G and C’ covers C, then C is normal in C’ and C’/C is order-isomorphic to a subgroup of the naturally ordered additive group of real numbers.
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Ordered sets and ordered groups
1996Abstract The fundamental notion that will inform our work is that of order: we shall be concerned with ordered sets, ordered groups, and ordered fields, and so, in due course, we shall specify how various algebraic operations interact with order structures.
H Garth Dales, W Hugh Woodin
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Proceedings of the London Mathematical Society, 1951
Britton, J. L., Shepperd, J. A. H.
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Britton, J. L., Shepperd, J. A. H.
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Cancer statistics for adolescents and young adults, 2020
Ca-A Cancer Journal for Clinicians, 2020Kimberly D Miller +2 more
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