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A composition formula in the rank two free group
Author(s):
Francisco
González-Acuña;
Arturo
Ramírez
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2779-2782.
MSC (1991):
Primary 57M07, 20E05
Posted:
May 4, 1999
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Abstract:
Using the fundamental group of a punctured torus, a free group of rank two, and the fact that the natural eipmorphism from onto has as kernel the group of inner automorphisms of , we describe representatives of the conjugacy classes of generating pairs of and give explicit relations between them.
References:
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- M. Cohen, W. Metzler and A. Zimmermann, What Does a Basis of
Look Like?, Math. Ann. 257 (1981), 435-445. MR 82m:20028 - [LTZ]
- M. Lustig, E-M. Thiele and H. Zieschang,
the Free Product of Two Finite Cyclic , 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
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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:
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
Posted:
May 4, 1999
Communicated by:
Ronald A. Fintushel
Copyright of article:
Copyright
1999,
American Mathematical Society
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