# two definition in automorphism of group

Let $G$ be finite p-group and $\sigma \in Aut(G)$ (automorphism group). what does below symbols mean
1. $[G,\sigma]$ (commutator)
2. $C_G(\sigma)$ (centralizer)

$[G,\sigma] = \langle g^{-1}\sigma(g) \mid g \in G \rangle$.
$C_G(\sigma) = \{ g \in G \mid \sigma(g)=g \}$ (which is a subgroup of $G$).