Geodesic
A Short Combinatorial Proof of the Vaught Conjecture
Canadian mathematical bulletin, Tome 18 (1975) no. 4, pp. 607-608

Voir la notice de l'article provenant de la source Cambridge University Press

In [5] R. C. Lyndon gave the first proof of the Vaught conjecture: that if a, b9 and c are elements of a free group F such that a 2 b 2=c 2, then ab=ba. Lyndon's proof has been followed by many alternative proofs and generalizations [1, 2, 3, 4, 6, 8, 9, 10, 11, 13, 14] all of which involve rather long combinatorial arguments or group theoretical arguments of a noncombinatorial nature.This note provides a short, purely combinatorial proof of the Vaught conjecture. 
Edmunds, Charles C. A Short Combinatorial Proof of the Vaught Conjecture. Canadian mathematical bulletin, Tome 18 (1975) no. 4, pp. 607-608. doi: 10.4153/CMB-1975-108-0
@article{10_4153_CMB_1975_108_0,
     author = {Edmunds, Charles C.},
     title = {A {Short} {Combinatorial} {Proof} of the {Vaught} {Conjecture}},
     journal = {Canadian mathematical bulletin},
     pages = {607--608},
     year = {1975},
     volume = {18},
     number = {4},
     doi = {10.4153/CMB-1975-108-0},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-108-0/}
}
TY  - JOUR
AU  - Edmunds, Charles C.
TI  - A Short Combinatorial Proof of the Vaught Conjecture
JO  - Canadian mathematical bulletin
PY  - 1975
SP  - 607
EP  - 608
VL  - 18
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-108-0/
DO  - 10.4153/CMB-1975-108-0
ID  - 10_4153_CMB_1975_108_0
ER  - 
%0 Journal Article
%A Edmunds, Charles C.
%T A Short Combinatorial Proof of the Vaught Conjecture
%J Canadian mathematical bulletin
%D 1975
%P 607-608
%V 18
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1975-108-0/
%R 10.4153/CMB-1975-108-0
%F 10_4153_CMB_1975_108_0

[1] 1. Baumslag, G., On a problem of Lyndon, J. London Math. Soc. 35 (1960), 30–32. Google Scholar

[2] 2. Baumslag, G., Residual nilpotence and relations in free groups, J. Algebra 2 (1965), 271–282. Google Scholar

[3] 3. Baumslag, G. and Steinberg, A., Residual nilpotence and relations in free groups, Bull. Amer. Math. Soc. 70 (1964), 283–284. Google Scholar

[4] 4. Budnika, L. G. and Markov, Al. A., On F-semigroups with three generators, Math. Notes, 14(1974), 711–716. Google Scholar

[5] 5. Lyndon, R. C., The equation a2b2=c2 in free groups, Michigan Math. J. 6 (1959), 89–95. Google Scholar

[6] 6. Lyndon, R. C. and Schützenberger, M. P., The equation aM=bNcP in a free group, Michigan Math. J. 9 (1962), 289–298. Google Scholar

[7] 7. Magnus, W., Karrass, A., and Solitar, D., Combinatorial Group Theory, Pure and Applied Math. Vol. 13, Interscience, New York, 1966. Google Scholar

[8] 8. Schutzenberger, M. P., Sur l’équation a2+n=b2+mc2+p dans un group libre, C.R. Acad. Sci. Paris 248 (1959), 2435–2436. Google Scholar

[9] 9. Shenkman, E., The equation anhn=cn in a free group, Ann. of Math. (2) 70 (1959), 562–564. Google Scholar

[10] 10. Stallings, J., On certain relations in free groups, Notices Amer. Math. Soc. 6 (1959), 532. Google Scholar

[11] 11. Steinberg, A., Ph.D. thesis, N.Y.U., 1962. Google Scholar

[12] 12. Wicks, M. J., Commutators in free products, J. London Math. Soc. 37 (1962), 433–444. Google Scholar

[13] 13. Wicks, M. J., A general solution of binary homogenous equations over free groups, Pacific J. Math. 41 (1972), 543–561. Google Scholar

[14] 14. Wicks, M. J., A relation in free products, Proc. Second Internat. Conf. Theory of Groups, Canberra, 1973, 709–716. Google Scholar

Cité par Sources :