Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A composition formula
in the rank two free group


Authors: Francisco González-Acuña and Arturo Ramírez
Journal: Proc. Amer. Math. Soc. 127 (1999), 2779-2782
MSC (1991): Primary 57M07, 20E05
DOI: https://doi.org/10.1090/S0002-9939-99-05344-7
Published electronically: May 4, 1999
MathSciNet review: 1664378
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Using the fundamental group of a punctured torus, a free group $F$ of rank two, and the fact that the natural eipmorphism from $Aut F$ onto $Aut(F/F')$ has as kernel the group of inner automorphisms of $F$, we describe representatives of the conjugacy classes of generating pairs of $F$ and give explicit relations between them.


References [Enhancements On Off] (What's this?)

  • [CMZ] M. Cohen, W. Metzler and A. Zimmermann, What Does a Basis of $\emph{F(a,b)}$ Look Like?, Math. Ann. 257 (1981), 435-445. MR 82m:20028
  • [LTZ] M. Lustig, E-M. Thiele and H. Zieschang, $\emph{Primitive}$ $\emph{Elements}$ $\emph{in}$ the Free Product of Two Finite Cyclic $\emph{Groups}$, Abh. Math. Sem. Univ. Hamburg 65 (1995), 277-281. MR 96g:20035
  • [LS] R. Lyndon and P. Schupp, Combinatorial Group Theory, Springer-Verlag 1977. MR 58:28182
  • [N] J. Nielsen, Die Isomorphismen der allgemeinen, unendlichen Gruppe mit zwei Erzeugenden, Math. Ann. 78 (1918), 385-397.
  • [OZ] R. Osborne and H. Zieschang, Primitives in the Free Group on Two Generators, Invent. Math. 63 (1981), 17-24. MR 82i:20042
  • [SL] K. Stroyan and W. Luxemburg, Introduction to the theory of infinitesimals, Academic Press 1976. MR 58:10429

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 57M07, 20E05

Retrieve articles in all journals with MSC (1991): 57M07, 20E05


Additional Information

Francisco González-Acuña
Affiliation: Instituto de Matemáticas, UNAM, México D.F. 04510, Mexico; Cimat, Guanjuato AP 402 Guanajuato 36000, México
Email: fico@matem.unam.mx

Arturo Ramírez
Affiliation: Cimat, Guanjuato AP 402 Guanajuato 36000, México
Email: ramirez@fractal.cimat.mx

DOI: https://doi.org/10.1090/S0002-9939-99-05344-7
Keywords: Rank two free group, primitive words
Received by editor(s): September 15, 1997
Published electronically: May 4, 1999
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1999 American Mathematical Society

American Mathematical Society