| context | $\langle\!\langle G,\cdot\rangle\!\rangle$ … group |
| definition | $\mathrm{Inn}(G)\equiv\langle\!\langle \{h\mapsto g\cdot h\cdot g^{-1}\,\mid\,g\in G\},*\rangle\!\rangle$ |
| inclusion | $*$ … pointwise function product on $G^G$ |
Explicitly, pointwise function product means
$(\phi*\psi)(h):=\phi(h)\cdot\psi(h)$
Wikipedia: Automorphism