-- We exhibit normal subgroups of a free nilpotent group F of rank two and class three, which have isomorphic finite quotients but are not conjugate under any automorphism of F.
Presentiamo sottogruppi normali di un gruppo nilpotente libero di rango due e classe tre, tali che i corrispondenti quozienti siano finiti e fra loro isomorfi, ma non coniugati rispetto ad alcun automorfismo di F.
@article{BUMI_2007_8_10B_2_441_0, author = {Sandro Mattarei}, title = {A Note on Automorphisms of Free Nilpotent Groups}, journal = {Bollettino dell'Unione Matematica Italiana}, volume = {10-A}, year = {2007}, pages = {441-444}, zbl = {1167.20020}, mrnumber = {2339452}, language = {en}, url = {http://dml.mathdoc.fr/item/BUMI_2007_8_10B_2_441_0} }
Mattarei, Sandro. A Note on Automorphisms of Free Nilpotent Groups. Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007) pp. 441-444. http://gdmltest.u-ga.fr/item/BUMI_2007_8_10B_2_441_0/
[DH75] Dualitäten und Gruppen der Ordnung , Geometriae Dedicata, 4, no. 2/3/4 (1975), 215-220. | MR 401907
- ,[FJ86] 11, Springer-Verlag, Berlin, 1986. | MR 868860
- , Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol.[Gas55] Zu einem von B.H. und H. Neumann gestellten Problem, Math. Nachr., 14 (1955), 249-252. | MR 83993
,[Hal59] | MR 103215
, The theory of groups, The MacMillan Co., New York, N. Y., 1959.[Hup67] 134, Springer-Verlag, Berlin, 1967. | MR 224703
, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band[LGM02] 27, Oxford University Press, Oxford, 2002, Oxford Science Publications. | MR 1918951 | Zbl 1008.20001
- , The structure of groups of prime power order, London Mathematical Society Monographs. New Series, Vol.[MKS76] | MR 422434 | Zbl 0362.20023
- - , Combinatorial group theory, revised ed., Dover Publications Inc., New York, 1976, Presentations of groups in terms of generators and relations.[Sco91] Groups of prime power order as Frobenius-Wielandt complements, Trans. Amer. Math. Soc., 325, no. 2 (1991), 855-874. | MR 998129 | Zbl 0743.20013
,