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A Criterion for automorphisms of certain groups to be inner
Published online by Cambridge University Press: 09 April 2009
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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).
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- Copyright © Australian Mathematical Society 1976
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