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A property of subgroups of infinite index in a free group
Author:
G. N. Arzhantseva
Journal:
Proc. Amer. Math. Soc. 128 (2000), 3205-3210
MSC (2000):
Primary 20E07, 20F06, 20P05.
Posted:
May 11, 2000
MathSciNet review:
1694447
Full-text PDF Free Access
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Additional Information
Abstract: We prove that if  is a finitely generated subgroup of infinite index in a free group  , then, in a certain statistical meaning, the normal subgroup generated by ``randomly'' chosen elements  of  has trivial intersection with  .
- 1.
G.
N. Arzhantseva and A.
Yu. Ol′shanskiĭ, Generality of the class of groups in
which subgroups with a lesser number of generators are free, Mat.
Zametki 59 (1996), no. 4, 489–496, 638
(Russian, with Russian summary); English transl., Math. Notes
59 (1996), no. 3-4, 350–355. MR 1445193
(98k:20040), http://dx.doi.org/10.1007/BF02308683
- 2.
G. N. Arzhantseva, On the groups all of whose subgroups with fixed number of generators are free, Fundamental and Applied Mathematics, 3(3) (1997), 675-683 (in Russian).
- 3.
Leon
Greenberg, Discrete groups of motions, Canad. J. Math.
12 (1960), 415–426. MR 0115130
(22 #5932)
- 4.
Abraham
Karrass and Donald
Solitar, On finitely generated subgroups of a
free group, Proc. Amer. Math. Soc. 22 (1969), 209–213. MR 0245655
(39 #6961), http://dx.doi.org/10.1090/S0002-9939-1969-0245655-2
- 5.
Roger
C. Lyndon and Paul
E. Schupp, Combinatorial group theory, Springer-Verlag,
Berlin, 1977. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 89. MR 0577064
(58 #28182)
- 6.
Stuart
W. Margolis and John
C. Meakin, Free inverse monoids and graph immersions,
Internat. J. Algebra Comput. 3 (1993), no. 1,
79–99. MR
1214007 (94c:20105), http://dx.doi.org/10.1142/S021819679300007X
- 7.
John
R. Stallings, Topology of finite graphs, Invent. Math.
71 (1983), no. 3, 551–565. MR 695906
(85m:05037a), http://dx.doi.org/10.1007/BF02095993
- 1.
- G. N. Arzhantseva and A. Yu. Ol'shanskii, Generality of the class of groups in which subgroups with a lesser number of generators are free, Mat. Zametki, 59(4) (1996), 489-496 (in Russian), English translation in Math. Notes, 59(4) (1996), 350-355. MR 98k:20040
- 2.
- G. N. Arzhantseva, On the groups all of whose subgroups with fixed number of generators are free, Fundamental and Applied Mathematics, 3(3) (1997), 675-683 (in Russian).
- 3.
- L. Greenberg, Discrete groups of motions, Canad. J. Math., 12 (1960), 414-425. MR 22:5932
- 4.
- A. Karrass and D. Solitar, On finitely generated subgroups of a free group, Proc. Amer. Math. Soc., 22 (1969), 209-213. MR 39:6961
- 5.
- R. Lyndon and P. Schupp, Combinatorial Group Theory, Springer-Verlag, 1977. MR 58:28182
- 6.
- S. W. Margolis and J. C. Meakin, Free inverse monoids and graph immersions, Int. J. Algebra and Comput., 3(1) (1993), 79-99. MR 94c:20105
- 7.
- J. Stallings, Topology of finite graphs, Inv.Math., 71 (1983), 552-565. MR 85m:05037a
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Additional Information
G. N. Arzhantseva
Affiliation:
Section de Mathématiques, Université de Genève, CP 240, 1211 Genève 24, Switzerland
Email:
Goulnara.Arjantseva@math.unige.ch
DOI:
http://dx.doi.org/10.1090/S0002-9939-00-05508-8
PII:
S 0002-9939(00)05508-8
Keywords:
Free groups,
generic properties of groups,
labelled graphs
Received by editor(s):
January 15, 1999
Posted:
May 11, 2000
Additional Notes:
The work is supported by the Russian Foundation for Fundamental Research grant 96-01-0420 and by ISSEP grant a98-2146.
Communicated by:
Ronald M. Solomon
Article copyright:
© Copyright 2000 American Mathematical Society
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