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11.128 (1990)

Solved

A group $G$ is said to be a $K$-group if for every subgroup $A \leqslant G$ there exists a subgroup $B \leqslant G$ such that $A \cap B = 1$ and $\langle A, B \rangle = G$. Is it true that normal subgroups of $K$-groups are also $K$-groups?

Contributor: M. Emaldi

Progress

No, it is not (V. N. Obraztsov, J. Austral. Math. Soc. (Ser. A), 61, no. 2 (1996), 267–288).

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