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3.17 (1969)

Solved

a) Is a non-abelian group with a unique linear ordering necessarily simple?
b) Is a non-commutative orderable group simple if it has no non-trivial normal relatively convex subgroups?

Contributor: A. I. Kokorin

Progress

Not always, in both cases (V. V. Bludov, Algebra and Logic, 13 (1974), 343–360).

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