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9.17 (1984)

Partially Solved

Let $G$ be a locally normal residually finite group.
$\qquad$ a) Can $G$ be embedded in a direct product of finite groups when the factor group $G/[G, G]$ is a direct product of cyclic groups?
$\qquad$ b) Does there exist a normal subgroup $H$ of $G$ which is embeddable in a direct product of finite groups and is such that $G/H$ is a divisible abelian group?

Contributor: L. A. Kurdachenko

Progress

a) Not always (L. A. Kurdachenko, Math. Notes, 39 (1986), 273–279).

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