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12.6 (1992)

Open

Let $G$ be a finitely generated group and suppose that $H$ is a $p$-subgroup of $G$ such that $H$ contains no non-trivial normal subgroups of $G$ and $HX = XH$ for any subgroup $X$ of $G$. Is then $G/C_G(H^G)$ a $p$-group where $H^G$ is the normal closure of $H$?

Contributor: G. Busetto

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