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Inner Automorphism Group

A particular type of Automorphism Group which exists only for Groups. For a Group $G$, the inner automorphism group is defined by

\begin{displaymath}
\mathop{\rm Inn}\nolimits (G)=\{\sigma_a: a\in G\}\subset \mathop{\rm Aut}\nolimits (G)
\end{displaymath}

where $\sigma_a$ is an Automorphism of $G$ defined by

\begin{displaymath}
\sigma_a(x)=axa^{-1}.
\end{displaymath}

See also Automorphism, Automorphism Group




© 1996-9 Eric W. Weisstein
1999-05-26