THE AUTOMORPHISM TOWER OF A FREE GROUP

VLADIMIR TOLSTYKH

doi:10.1112/S0024610799008273

Abstract

It is proved that the automorphism group of any non-abelian free group F is complete. The key technical step in the proof is that the set of all conjugations by powers of primitive elements is first-order parameter-free definable in the group Aut(F).

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Formanek, Edward 2001. A question of B. Plotkin about the semigroup of endomorphisms of a free group. Proceedings of the American Mathematical Society, Vol. 130, Issue. 4, p. 935.

Mashevitzky, G. Plotkin, B. and Plotkin, E. 2004. Automorphisms of the category of free Lie algebras. Journal of Algebra, Vol. 282, Issue. 2, p. 490.

Bardakov, Valery Shpilrain, Vladimir and Tolstykh, Vladimir 2005. On the palindromic and primitive widths of a free group. Journal of Algebra, Vol. 285, Issue. 2, p. 574.

Важенин, Юрий Михайлович Vazhenin, Yurii Mikhailovich Пинус, Александр Георгиевич and Pinus, Aleksandr Georgievich 2005. Элементарная классификация и разрешимость теории производных структур. Успехи математических наук, Vol. 60, Issue. 3, p. 3.

TOLSTYKH, VLADIMIR 2009. Infinitely generated free nilpotent groups: completeness of the automorphism groups. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 147, Issue. 3, p. 541.

Tolstykh, Vladimir 2011. Small conjugacy classes in the automorphism groups of relatively free groups. Journal of Pure and Applied Algebra, Vol. 215, Issue. 9, p. 2086.

Kunyavskiĭ, Boris 2013. Local–global invariants of finite and infinite groups: Around Burnside from another side. Expositiones Mathematicae, Vol. 31, Issue. 3, p. 256.

ATABEKYAN, V. S. 2013. THE GROUPS OF AUTOMORPHISMS ARE COMPLETE FOR FREE BURNSIDE GROUPS OF ODD EXPONENTS n ≥ 1003. International Journal of Algebra and Computation, Vol. 23, Issue. 06, p. 1485.

Tolstykh, Vladimir 2014. On the outer automorphism groups of free groups. Journal of Algebra, Vol. 420, Issue. , p. 120.

Atabekyan, V. S. 2015. Automorphism Groups and Endomorphism Semigroups of Groups B(m, n). Algebra and Logic, Vol. 54, Issue. 1, p. 58.

Atabekyan, V. S. and Aslanyan, H. T. 2018. The automorphisms of endomorphism semigroups of relatively free groups. International Journal of Algebra and Computation, Vol. 28, Issue. 02, p. 207.

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THE AUTOMORPHISM TOWER OF A FREE GROUP

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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THE AUTOMORPHISM TOWER OF A FREE GROUP

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