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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
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$.

References [Enhancements On Off] (What's this?)

  • [1] C. F. Miller and P. E. Schupp, Embeddings into Hopfian groups, J. Algebra 17 (1971), 171-176. MR 0269728 (42:4623)
  • [2] P. E. Schupp, A survey of small cancellation theory, Word Problems and the Burnside Problem (Boone, Cannonito, Lyndon eds.), North-Holland, 1972, pp. 569-589. MR 0412289 (54:415)

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Article copyright: © Copyright 1987 American Mathematical Society

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