Strongly closed subgroup

Definition with symbols
Let $$H \le K \le G$$ be groups. Then, $$H$$ is said to be strongly closed in $$K$$ with respect to $$G$$ if any $$G$$-conjugate of an element of $$H$$, which lies inside $$K$$, in fact lies inside $$H$$. In other words, for any $$g \in G$$:

$$gHg^{-1} \cap K \le H$$.

The term is typically used for the situation where $$K$$ is a Sylow subgroup of $$G$$. The particular case can also be generalized to the notion of a strongly closed subgroup for a fusion system.

Weaker properties

 * Stronger than::Weakly closed subgroup