Definition:Group of Outer Automorphisms/Warning

Warning

The name group of outer automorphisms is a misnomer, because:

$(1): \quad$ the elements of $\dfrac {\Aut G} {\Inn G}$ are not outer automorphisms of $G$

and

$(2): \quad$ the outer automorphisms of $G$ do not themselves form a group.

Sources

• 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $2$: Group Homomorphism and Isomorphism: $\S 64 \alpha$