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20.75 (2022)

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Let $G$ be a finite $p$-group and assume that all abelian normal subgroups of $G$ can be generated by $k$ elements. Is it true that every abelian subgroup of $G$ can be generated by $2k$ elements?

The $k$-th direct power of $D_{16}$ shows that this bound would be best possible.

Contributor: L. Pyber

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