Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-27T10:51:46.872Z Has data issue: false hasContentIssue false
  • English
  • Français

Presentations of the Free Metabelian Group of Rank 2

Published online by Cambridge University Press:  20 November 2018

Martin J. Evans
Martin J. Evans*
Affiliation:
Department of Mathematics, University of Alabama Tuscaloosa, Alabama 35487 U.S.A.
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 F3 denote the free group of rank 3 and M2 denote the free metabelian group of rank 2. We say that x * F3 is a primitive element of F3 if it can be included a in some basis of F3. We establish the existence of presentations such that N does not contain any primitive elements of F3.

Keywords

20F05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 37 , Issue 4 , 01 December 1994 , pp. 468 - 472
Copyright
Copyright © Canadian Mathematical Society 1994

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.+4,+Trans.+Amer.+Math.+Soc.+292(1985),+81–101.>Google Scholar
3. Evans, Martin J., Presentations of groups involving more generators than are necessary, Proc. London Math. Soc. (3) 67(1993), 106–126.Google Scholar
4. Gupta, C. K., Gupta, N. D. and Noskov, G. A., Some applications of Artamonov-Quillen-Suslin theorems to metabelian inner rank andprimitivity, Canad. J. Math. 46(1994), 298–307.Google Scholar
5. Higman, G., The units of group rings, Proc. London Math. Soc. (2) 46(1940), 231–248.Google Scholar
6. Mochizuki, H. Y., Automorphisms of solvable groups, Part II, Proc. Groups, St. Andrews, London Math. Soc. Lecture Notes Series 121, 1985.Google Scholar
7. Roman'kov, V. A., Primitive elements of free groups of rank 3, Mat. Sb. (7) 182(1991), 1074–1085.Google Scholar