Abstract
A negative answer is given to a question posed by E. Schenkman and F. Haimo: does every torsion-free nilpotent group have an outer automorphism?
Similar content being viewed by others
Literature cited
R. Ree, “The existence of outer automorphisms of some groups. I,” Proc. Amer. Math. Soc.,7, No. 6, 962–964 (1956).
B. I. Plotkin, Groups of Automorphisms of Algebraic Systems [in Russian], Moscow (1966).
R. Ree, “The existence of outer automorphisms of some groups. II,” Proc. Amer. Math. Soc.,9, No. 1, 105–109 (1958).
W. Gaschütz, “Kohomologische Trivialitäten und äusser Automorphismen von p-Gruppen,” Math. Zeitschr.,88, No. 5, 432–433 (1965).
W. Gaschütz, “Nicht-abelische p-Gruppen bezitzen äussere p-Automorphismen,” J. Algebra,4, No. 1, 1–2 (1966).
A. G. Kurosh, Theory of Groups [English translation], Chelsea, New York (1955–6).
A. E. Zalesskii, “A nilpotent p-group possesses an outer automorphism,” Dokl. Akad. Nauk SSSR,196, No. 4, 751–754 (1971).
Author information
Authors and Affiliations
Additional information
Translated from Matematicheskie Zametki, Vol. 11, No. 1, pp. 21–26, January, 1972.
Rights and permissions
About this article
Cite this article
Zalesskii, A.E. An example of a torsion-free nilpotent group having no outer automorphisms. Mathematical Notes of the Academy of Sciences of the USSR 11, 16–19 (1972). https://doi.org/10.1007/BF01366910
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01366910