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18.85 (2014)

Open

A subset of a group is said to be rational if it can be obtained from finite subsets by finitely many rational operations, that is, taking union, product, and the submonoid generated by a set.

Conjecture: every finitely generated solvable group in which all rational subsets form a Boolean algebra is virtually abelian.

Contributor: V. A. Roman’kov

Progress

This is known to be true if the group is metabelian, or polycyclic, or of finite rank (G. A. Bazhenova).

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