Definition:Conjugacy Action/Subgroups

Definition

Let $X$ be the set of all subgroups of $G$.

The (left) conjugacy action on subgroups is the group action $* : G \times X \to X$:

$g * H = g \circ H \circ g^{-1}$

The right conjugacy action on subgroups is the group action $* : X \times G \to X$:

$H * g = g^{-1} \circ H \circ g$

Also see

• Conjugacy Action is Group Action