# Category:Definitions/Weakly Pronormal Subgroups

This category contains definitions related to Weakly Pronormal Subgroups.
Related results can be found in Category: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 $x$.

## Pages in category "Definitions/Weakly Pronormal Subgroups"

The following 3 pages are in this category, out of 3 total.