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2.70 (1966)

Solved

a) Let a group $G$ be the product of two subgroups $A$ and $B$, each of which is locally cyclic and torsion-free. Prove that either $A$ or $B$ has a non-trivial subgroup that is normal in $G$.

b) Characterize the groups that can be factorized in this way.

Contributor: N. F. Sesekin

Progress

a) This was proved (D. I. Zaitsev, Algebra and Logic, 19 (1980), 94–106).

b) They were characterized (Ya. P. Sysak, Algebra and Logic, 25 (1986), 425–433).

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