Аннотация
Partially ordered groups, also known as po-groups, are groups with a compatible partial order. Results from M.\,I. Zajceva and H.-H.\ Teh are combined in order to provide a full characterisation of linear order extensions of a given order on a group. In contrast to Teh this approach provides a method to discuss linear orders of different Abelian rank in a uniform manner. This will be achieved by modelling the linear orders as hyperplanes in a real vector space.
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