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3.18 (1969)

Solved

(B. H. Neumann). A group $U$ is called universal for a class $\mathfrak{K}$ of groups if $U$ contains an isomorphic image of every member of $\mathfrak{K}$. Does there exist a countable group that is universal for the class of countable orderable groups?

Contributor: A. I. Kokorin

Progress

No (M. I. Kargapolov, Algebra and Logic, 9 (1970), 257–261; D. B. Smith, Pacific J. Math., 35 (1970), 49–502).

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