A characterization of inner automorphisms
HTML articles powered by AMS MathViewer
- by Paul E. Schupp PDF
- Proc. Amer. Math. Soc. 101 (1987), 226-228 Request permission
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
- Charles F. Miller III and Paul E. Schupp, Embeddings into Hopfian groups, J. Algebra 17 (1971), 171–176. MR 269728, DOI 10.1016/0021-8693(71)90028-7
- Paul E. Schupp, A survey of small cancellation theory, Word problems: decision problems and the Burnside problem in group theory (Conf. on Decision Problems in Group Theory, Univ. California, Irvine, Calif. 1969; dedicated to Hanna Neumann), Studies in Logic and the Foundations of Math., Vol. 71, North-Holland, Amsterdam, 1973, pp. 569–589. MR 0412289
Additional Information
- © Copyright 1987 American Mathematical Society
- 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