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8.31 (1982)

Solved

Describe the finite groups in which every proper subgroup has a complement in some larger subgroup. Among these groups are, for example, $\text{PSL}_2(7)$ and all Sylow subgroups of symmetric groups.

Contributor: V. M. Levchuk

Progress

These groups are described independently in (V. M. Levchuk, A. G. Likharev, Siberian Math. J., 47, no. 4 (2006), 659–668) and in (V. N. Tyutyanov, Proc. Gomel’ State Univ., 3 (2006), 178–183 (in Russian)).

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