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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A characterization of inner automorphisms


Author: Paul E. Schupp
Journal: Proc. Amer. Math. Soc. 101 (1987), 226-228
MSC: Primary 20E36
DOI: https://doi.org/10.1090/S0002-9939-1987-0902532-X
MathSciNet review: 902532
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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 $ \alpha $ be an automorphism of $ G$. The automorphism $ \alpha $ is an inner automorphism of $ G$ if and only if $ \alpha $ has the property that whenever $ G$ is embedded in a group $ H$, then $ \alpha $ extends to some automorphism of $ H$.


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DOI: https://doi.org/10.1090/S0002-9939-1987-0902532-X
Article copyright: © Copyright 1987 American Mathematical Society