A characterization of inner automorphisms
Paul E. Schupp
Proc. Amer. Math. Soc. 101 (1987), 226-228
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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 .
F. Miller III and Paul
E. Schupp, Embeddings into Hopfian groups, J. Algebra
17 (1971), 171–176. MR 0269728
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.
0412289 (54 #415)
- C. F. Miller and P. E. Schupp, Embeddings into Hopfian groups, J. Algebra 17 (1971), 171-176. MR 0269728 (42:4623)
- 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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