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15.33 (2002)

Solved

Suppose that all 2-generator subgroups of a finite 2-group $G$ are metacyclic. Is the derived length of $G$ bounded? This is true for finite $p$-groups if $p \neq 2$, see 1.1.8 in (M. Suzuki, Structure of a group and the structure of its lattice of subgroups, Springer, Berlin, 1956).

Contributor: Ya. G. Berkovich

Progress

Yes, it is at most 2 (E. Crestani, F. Menegazzo, J. Group Theory, 15, no. 3 (2012), 359–383).

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