RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Journal history Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Fundam. Prikl. Mat.: Year: Volume: Issue: Page: Find

 Fundam. Prikl. Mat., 1997, Volume 3, Issue 3, Pages 675–683 (Mi fpm237)

On the groups in which the subgroups with fixed number of generators are free

G. N. Arzhantseva

M. V. Lomonosov Moscow State University

Abstract: We prove here that, in a definite statistical meaning, in almost every group with $m$ generators and $n$ relations (we suppose $m$ and $n$ to be fixed) all $\le L$-generated subgroups of infinite index are free ($L$ is an arbitrary preassigned bound, possibly $L\gg m$) and all subgroups of finite index are not free. To prove this fact we found the condition on relations which guarantee that all subgroups of infinite index with fixed number of generators in a finitely presented group are free. This condition is formulated by means of the finite marked graphs.

Full text: PDF file (417 kB)

Bibliographic databases:
UDC: 519.40

Citation: G. N. Arzhantseva, “On the groups in which the subgroups with fixed number of generators are free”, Fundam. Prikl. Mat., 3:3 (1997), 675–683

Citation in format AMSBIB
\Bibitem{Arz97} \by G.~N.~Arzhantseva \paper On the groups in which the subgroups with fixed number of generators are free \jour Fundam. Prikl. Mat. \yr 1997 \vol 3 \issue 3 \pages 675--683 \mathnet{http://mi.mathnet.ru/fpm237} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1794135} \zmath{https://zbmath.org/?q=an:0929.20025} 

• http://mi.mathnet.ru/eng/fpm237
• http://mi.mathnet.ru/eng/fpm/v3/i3/p675

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Arzhantseva, GN, “Generic properties of finitely presented groups and Howson's theorem”, Communications in Algebra, 26:11 (1998), 3783
2. Arzhantseva, GN, “A property of subgroups of infinite index in a free group”, Proceedings of the American Mathematical Society, 128:11 (2000), 3205
3. Bumagin, I, “On small cancellation k-generated groups with (k-1)-generated subgroups all free”, International Journal of Algebra and Computation, 11:5 (2001), 507
4. Kapovich, I, “Generic-case complexity, decision problems in group theory, and random walks”, Journal of Algebra, 264:2 (2003), 665
5. Ghys, T, “Random groups (after Misha Gromov,...)”, Asterisque, 2004, no. 294, 173
6. Kapovich, I, “Bounded rank subgroups of Coxeter groups, Artin groups and one-relator groups with torsion”, Proceedings of the London Mathematical Society, 88 (2004), 89
7. Kapovich, I, “Delzant's T-invariant, Kolmogorov complexity and one-relator groups”, Commentarii Mathematici Helvetici, 80:4 (2005), 911
8. Kapovich, I, “Genericity, the Arzhantseva-Ol'shanskii method and the isomorphism problem for one-relator groups”, Mathematische Annalen, 331:1 (2005), 1
9. Kapovich, I, “Average-case complexity and decision problems in group theory”, Advances in Mathematics, 190:2 (2005), 343
10. Kapovich, I, “Generic properties of Whitehead's algorithm and isomorphism rigidity of random one-relator groups”, Pacific Journal of Mathematics, 223:1 (2006), 113
11. Kapovich, I, “Densities in free groups and Z(k) visible points and test elements”, Mathematical Research Letters, 14:2–3 (2007), 263
12. Kaimanovich, V, “The subadditive ergodic theorem and generic stretching factors for free group automorphisms”, Israel Journal of Mathematics, 157:1 (2007), 1
13. Kapovich, I, “On group-theoretic models of randomness and genericity”, Groups Geometry and Dynamics, 2:3 (2008), 383
14. Kapovich, I, “Random quotients of the modular group are rigid and essentially incompressible”, Journal fur Die Reine und Angewandte Mathematik, 628 (2009), 91
15. V. N. Bezverkhnii, I. V. Dobrynina, “O svobodnykh podgruppakh v gruppakh Artina s drevesnoi strukturoi”, Chebyshevskii sb., 15:1 (2014), 32–42
•  Number of views: This page: 228 Full text: 94 First page: 2