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* *be a group and let* *be an automorphism of* . *The automorphism* *is an inner automorphism of* *if and only if* *has the property that whenever* *is embedded in a group* , *then* *extends to some automorphism of* .

**[1]**Charles F. Miller III and Paul E. Schupp,*Embeddings into Hopfian groups*, J. Algebra**17**(1971), 171–176. MR**0269728****[2]**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), North-Holland, Amsterdam, 1973, pp. 569–589. Studies in Logic and the Foundations of Math., Vol. 71. MR**0412289**

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DOI:
https://doi.org/10.1090/S0002-9939-1987-0902532-X

Article copyright:
© Copyright 1987
American Mathematical Society