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A Criterion for automorphisms of certain groups to be inner

Published online by Cambridge University Press:  09 April 2009

Joan L. Dyer
Joan L. Dyer
Affiliation:
Institute for Advanced Study Princeton, New Jersey, U.S.A. Lehman CollegeC.U.N.Y. New York, U.S.A.
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Let R be a normal subgroup of the free group F, and set G = F/[R, R]. We assume that F/R is a torsion-free group which is either solvable and not cyclic, or has a non-trivial center and is not cyclic-by-periodic. Then any automorphism of G whose restriction to R/[R, R] is trivial is an inner automorphism, determined by some element of R/[R, R]. This result extends a theorem of Šmel'kin (1967).

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 2 , March 1976 , pp. 179 - 184
Copyright
Copyright © Australian Mathematical Society 1976

References

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