Pseudocomplete nilpotent groups

Fournelle, Thomas A.

doi:10.1090/S0002-9939-1983-0691267-3

Pseudocomplete nilpotent groups
HTML articles powered by AMS MathViewer

by Thomas A. Fournelle PDF

Proc. Amer. Math. Soc. 88 (1983), 1-7 Request permission

Abstract:

Semicomplete nilpotent groups, that is, nilpotent groups with no outer automorphisms, have been of interest for many years. In this paper pseudocomplete nilpotent groups, that is, nilpotent groups in which the automorphism group and the inner automorphism group are isomorphic (not equal), are constructed. When suitable conditions are placed on the pseudocomplete nilpotent group, the quotient of the automorphism group by the inner automorphism group is completely characterized.

References

Torsion in semicomplete nilpotent groups

Infinite Abelian groups

Wolfgang Gaschütz, Nichtabelsche $p$-Gruppen besitzen äussere $p$-Automorphismen, J. Algebra 4 (1966), 1–2 (German). MR 193144, DOI 10.1016/0021-8693(66)90045-7
Hermann Heineken, Automorphism groups of torsionfree nilpotent groups of class two, Symposia Mathematica, Vol. XVII (Convegno sui Gruppi Infiniti, INDAM, Roma, 1973) Academic Press, London, 1976, pp. 235–250. MR 0419627
Rimhak Ree, The existence of outer automorphisms of some groups, Proc. Amer. Math. Soc. 7 (1956), 962–964. MR 82987, DOI 10.1090/S0002-9939-1956-0082987-6

Outer automorphisms of torsion-free nilpotent groups

Urs Stammbach, Homology in group theory, Lecture Notes in Mathematics, Vol. 359, Springer-Verlag, Berlin-New York, 1973. MR 0382477
Robert B. Warfield Jr., Nilpotent groups, Lecture Notes in Mathematics, Vol. 513, Springer-Verlag, Berlin-New York, 1976. MR 0409661
A. E. Zalesskiĭ, A nilpotent $p$-group possesses an outer automorphism, Dokl. Akad. Nauk SSSR 196 (1971), 751–754 (Russian). MR 0274587
A. E. Zalesskiĭ, An example of a nilpotent group without torsion that has no outer automorphisms, Mat. Zametki 11 (1972), 21–26 (Russian). MR 291291