Proceedings of the American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support My Subscriptions Help
ISSN 1088-6826(e) ISSN 0002-9939(p)

Equations in free groups are not finitely approximable

Author(s): Thierry Coulbois; Anatole Khelif
Journal: Proc. Amer. Math. Soc. 127 (1999), 963-965.
MSC (1991): Primary 20F10, 03B25, 20E18
MathSciNet review: 1485465
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: We give an equation in any free group of rank $\geq 2$ that has a solution in any finite quotient of , but has no solution in .

References:

1.: G. Baumslag, Residual nilpotency and relations in free groups, J. of Algebra 2 (1965) 271-282. MR 31:3487
2.: B. Hartley, Subgroups of finite index in profinite groups, Mathematische Zeitschrift 168 (1979) 71-76. MR 80k:20028
3.: A. Khelif, Some properties of free groups and their profinite completions, in preparation.
4.: G.S. Makanin, Equations in a free group, Math. USSR Izv. 21 (1983) 483-546. MR 84m:20040
5.: C. Martinez, On power subgroups of profinite groups , Trans. of the A. M. S. 345 (1994) 865-869. MR 95d:20053
6.: M.P. Schützenberger, Sur l'equation $a^{2+n}= b^{2+m}c^{2+p}$ dans un groupe libre, Comptes Rend. de l'Ac. des Sciences (Paris) 248 (1959) 2435-2436. MR 21:2000
7.: M.R. Vaughan-Lee, The restricted Burnside problem, London Math. Soc., Oxford 1990. MR 92c:20001

	Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
\|