inner automorphism


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inner automorphism

[¦in·ər ‚ȯd·ō′mȯr·fiz·əm]
(mathematics)
An automorphism h of a group where h (g) = g0-1· g · g0, for every g in the group with g0 some fixed group element.
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An inner automorphism [theta] is one such that there exists u [member of] U(M) for which [theta](x) = uxu* for all x [member of] M.
We have just shown that all inner automorphisms of [?
Consider now the inner automorphism of R induced by the invertible matrix P = I + [e.
On the other hand, if [chi] is the inner automorphisms induced by the invertible matrix Q = I + [e.
V]> = 0 for some compact neighborhood V of G invariant under the inner automorphisms.
This class consists indeed of the inner automorphisms, defined by
The explicit definition makes evident some extra-features of the inner automorphisms, which are described in the next lemma: a proof is provided just for the reader convenience.
All the automorphisms of H are inner automorphisms.