  Consider a group $G$ acting on a set $\Omega$, the vector $v_{a,b}$ is a
vector with the entries indexed by the elements of $G$, and the $g$-entry is 1
if $g$ maps $a$ to $b$, and zero otherwise. A $(G,\Omega)$-Cameron-Liebler set
is a subset of $G$, whose indicator function is a linear combination of
elements in $\{v_{a, b}\ :\ a, b \in \Omega\}$. We investigate Cameron-Liebler
sets in permutation groups, with a focus on constructions of Cameron-Liebler
sets for 2-transitive groups.
