Conjugacy-closed subgroup

In group theory, a subgroup \( H \) of a group \( G \) is called **conjugacy-closed** if, for every element \( h \) in \( H \) and every element \( g \) in \( G \), the conjugate \( g h g^{-1} \) is also in \( H \) whenever \( h \) is in \( H \).