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A Characterization of Inner Automorphisms

Paul E. Schupp
Proceedings of the American Mathematical Society
Vol. 101, No. 2 (Oct., 1987), pp. 226-228
DOI: 10.2307/2045986
Stable URL: http://www.jstor.org/stable/2045986
Page Count: 3
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A Characterization of Inner Automorphisms
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Abstract

It turns out that one can characterize inner automorphisms without mentioning either conjugation or specific elements. We prove the following THEOREM Let G be a group and let α be an automorphism of G. The automorphism α is an inner automorphism of G if and only if α has the property that whenever G is embedded in a group H, then α extends to some automorphism of H.

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