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Proceedings of the American Mathematical Society
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
Published electronically: May 4, 1999
MathSciNet review: 1664378
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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.


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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: http://dx.doi.org/10.1090/S0002-9939-99-05344-7
PII: S 0002-9939(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