PlanetMath: a nontrivial normal subgroup of a finite $p$-group $G$ and the center of $G$ have nontrivial intersection

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a nontrivial normal subgroup of a finite $p$

-group

and the center of $G$

have nontrivial intersection

(Theorem)

Let $G$ be a finite $p$ group, and let $H$ be a nontrivial normal subgroup of $G$ Then $H\cap Z(G) \neq \{1\}$

"a nontrivial normal subgroup of a finite $p$

-group

and the center of $G$

have nontrivial intersection" is owned by gumau.

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Attachments:: proof that a nontrivial normal subgroup of a finite -group and the center of have nontrivial intersection (Proof) by rm50

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20D20 (Group theory and generalizations :: Abstract finite groups :: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure)

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