Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-18T01:53:06.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Primitivity in Free Groups and Free Metabelian Groups

Published online by Cambridge University Press:  20 November 2018

C. K. Gupta ,
N. D. Gupta  and
V. A. Roman'kov
C. K. Gupta
Affiliation:
University of Manitoba Winnipeg, Manitoba R3T2N2
N. D. Gupta
Affiliation:
University of Manitoba Winnipeg, Manitoba R3T2N2
V. A. Roman'kov
Affiliation:
Kompleksny Otdel Pr. Mira 19-a Omsk 644050 USSR
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let Mn, c denote the free n-generator metabelian nilpotent group of class c. For m ≤ n – 2, every primitive system of m elements of Mn, c can be lifted to a primitive system of m elements of the absolutely free group Fn of rank n. The restriction on m cannot be improved.

Keywords

20F2820F18
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 3 , 01 June 1992 , pp. 516 - 523
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Bachmuth, S., Automorphisms of free metabelian groups, Trans. Amer. Math. Soc. 118 (1965), 93–104.Google Scholar
2. Bachmuth, S. and Mochizuki, H.Y., Aut(F) → Aut(F/ F“) is surjective for free group F of rank ≥ 4, Trans. Amer. Math. Soc. 292 (1985), 81–101.Google Scholar
3. Birman, Joan S., An inverse function theorem for free groups, Proc. Amer. Math. Soc. 41 (1974), 634–638.Google Scholar
4. Chein, Orin, IA automorphisms of free and free metabelian groups, Comm. Pure Appl. Math. 21 (1968), 605–629.Google Scholar
5. Gupta, Narain, Free group rings, Contemporary Math. 66 (1987), Amer. Math. Soc.Google Scholar
6. Lyndon, Roger C. and Paul Schupp, E., Combinatorial group theory, Ergebnisse Math. Grenzgeb. 89 (1977), Springer- Verlag.Google Scholar
7. Roman'kov, V.A., The automorphism groups of free metabelian groups. Questions on pure and applied algebra. Proc. Computer Centre, USSR Academy of Sciences, Novosibirsk, 1985. 35–81. Russian.Google Scholar
8. Timoshenko, E.I., Algorithmic problems for metabelian groups, Algebra and Logic 12 1973 132–137.(Russian Edition: Algebra i Logika 12 (1973), 232–240.Google Scholar
9. Timoshenko, E.I., On embedding of given elements into a basis of free metabelian groups, Russian, preprint.Google Scholar
10. Umirbaev, U.U., On primitive systems of elements in free groups, to appear.Google Scholar