# Category:Weakly Pronormal Subgroups

This category contains results about Weakly Pronormal Subgroups.
Definitions specific to this category can be found in Definitions/Weakly Pronormal Subgroups.

$H$ is weakly pronormal in $G$ if and only if:

$\forall g \in G: \exists x \in H^{\gen g}: H^x = H^g$

where:

$H^{\gen g}$ denotes the smallest subgroup of $G$ containing $H$, generated by the conjugacy action by the cyclic subgroup of $G$ generated by $g$
$H^x$ denotes the conjugate of $H$ by $x$.

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