2009
DOI: 10.1017/s0305004109990077
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Infinitely generated free nilpotent groups: completeness of the automorphism groups

Abstract: Abstract. We transfer the results of Dyer, Formanek and Kassabov on the automorphism towers of finitely generated free nilpotent groups to infinitely generated free nilpotent groups. We prove that the automorphism groups of infinitely generated free nilpotent groups are complete. By combining the results of Dyer, Formanek, Kassabov with the results in the present paper, one gets that the automorphism tower of any free nilpotent group terminates after finitely many steps. IntroductionBaumslag conjectured in the… Show more

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Cited by 3 publications
(1 citation statement)
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“…• The subgroup Inn(F ∞ ) is then first-order definable in Aut(F ∞ ). Theorem 8 (Tolstykh [17], [18]). For any k ≥ 2, the automorphism group Aut(N ∞,k ) of any free nilpotent group N ∞,k of infinite rank is complete.…”
Section: Other Propertiesmentioning
confidence: 99%
“…• The subgroup Inn(F ∞ ) is then first-order definable in Aut(F ∞ ). Theorem 8 (Tolstykh [17], [18]). For any k ≥ 2, the automorphism group Aut(N ∞,k ) of any free nilpotent group N ∞,k of infinite rank is complete.…”
Section: Other Propertiesmentioning
confidence: 99%