Asymptotic growth and least common multiples in groups
By K. Bou-Rabee, D. McReynolds. 2009
54 citations recorded by the source corpus.
In this article, we relate word and normal subgroup growth to certain functions that arise in the quantification of residual finiteness. One consequence of this endeavor is a pair of results that equate the virtual nilpotency of a finitely generated group with the asymptotic behavior of these functions. The second half of this article investigates the asymptotic behavior of two of these functions. Our main result in this area resolves a question of Bogopolski from the Kourovka notebook concerning lower bounds of one of these functions for non‐abelian free groups.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/b2aab93ae4afd576ebc5bf41334c13e8d0feaf05
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Bounding the residual finiteness of free groups (2009, background): “ the following question in the Kourovka notebook [8]. Question 20. Does there exist a C = C(k) > 0 such that DF k (w) ≤ C log(|w|)? 6 MARTIN KASSABOV AND FRANCESCO MATUCCI Bou-Rabee and McReynolds [1] showed that this question has a negative answer establishing the following result on the lower b”