A Note on Automorphisms of Free Nilpotent Groups

Sandro Mattarei

Bollettino dell'Unione Matematica Italiana (2007)

  • Volume: 10-B, Issue: 2, page 441-444
  • ISSN: 0392-4033

Abstract

top
-- 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.

How to cite

top

Mattarei, Sandro. "A Note on Automorphisms of Free Nilpotent Groups." Bollettino dell'Unione Matematica Italiana 10-B.2 (2007): 441-444. <http://eudml.org/doc/290368>.

@article{Mattarei2007,
abstract = {-- 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.},
author = {Mattarei, Sandro},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {6},
number = {2},
pages = {441-444},
publisher = {Unione Matematica Italiana},
title = {A Note on Automorphisms of Free Nilpotent Groups},
url = {http://eudml.org/doc/290368},
volume = {10-B},
year = {2007},
}

TY - JOUR
AU - Mattarei, Sandro
TI - A Note on Automorphisms of Free Nilpotent Groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2007/6//
PB - Unione Matematica Italiana
VL - 10-B
IS - 2
SP - 441
EP - 444
AB - -- 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.
LA - eng
UR - http://eudml.org/doc/290368
ER -

References

top
  1. DAUES, G. - HEINEKEN, H., Dualitäten und Gruppen der Ordnung p 6 , Geometriae Dedicata, 4, no. 2/3/4 (1975), 215-220. MR401907DOI10.1007/BF00148755
  2. FRIED, M. D. - JARDEN, M., Field arithmetic, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 11, Springer-Verlag, Berlin, 1986. MR868860DOI10.1007/978-3-662-07216-5
  3. GASCHÜTZ, W., Zu einem von B.H. und H. Neumann gestellten Problem, Math. Nachr., 14 (1955), 249-252. MR83993DOI10.1002/mana.19550140406
  4. HALL, M., The theory of groups, The MacMillan Co., New York, N. Y., 1959. MR103215
  5. HUPPERT, B., Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin, 1967. MR224703
  6. LEEDHAM-GREEN, C. R. - MCKAY, S., The structure of groups of prime power order, London Mathematical Society Monographs. New Series, Vol. 27, Oxford University Press, Oxford, 2002, Oxford Science Publications. Zbl1008.20001MR1918951
  7. MAGNUS, W. - KARRASS, A. - SOLITAR, D., Combinatorial group theory, revised ed., Dover Publications Inc., New York, 1976, Presentations of groups in terms of generators and relations. Zbl0362.20023MR422434
  8. SCOPPOLA, C. M., Groups of prime power order as Frobenius-Wielandt complements, Trans. Amer. Math. Soc., 325, no. 2 (1991), 855-874. Zbl0743.20013MR998129DOI10.2307/2001651

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.