Affiliation:
1. Open Space, Schreiber Building (Mathematics) Tel-Aviv University , Levanon Street , Tel Aviv , Israel
Abstract
Abstract
We show that given a finitely generated LERF group G with positive rank gradient, and finitely generated subgroups A, B ≤ G of infinite index, one can find a finite index subgroup B
0 of B such that [G : 〈A ∪ B
0〉] = ∞. This generalizes a theorem of Olshanskii on free groups. We conclude that a finite product of finitely generated subgroups of infinite index does not cover G. We construct a transitive virtually faithful action of G such that the orbits of finitely generated subgroups of infinite index are finite. Some of the results extend to profinite groups with positive rank gradient.
Reference15 articles.
1. Abert, M.—Gelander, T.—Nikolov, N.: Rank, combinatorial cost and homology torsion growth in higher rank lattices, (2015), preprint.
2. Abert, M.—Jaikin-Zapirain, A.—Nikolov, N.: The rank gradient from a combinatorial viewpoint, Groups Geom. Dyn. 5 (2011), 213–230.
3. Abert, M.—Nikolov, N.: Rank gradient, cost of groups and the rank versus Heegaard genus problem, J. Eur. Math. Soc. 14 (2012), 1657–1677.10.4171/JEMS/344
4. Chaynikov, V.: Actions of maximal growth of hyperbolic groups, (2012), preprint.
5. de Cornulier, Y.: Finitely presented wreath products and double coset decompositions, Geom. Dedic. 122 (2006), 89–108.10.1007/s10711-006-9061-4
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Virtual retraction and Howson’s theorem in pro-$p$ groups;Transactions of the American Mathematical Society;2019-12-04