Quantifying residual finiteness
By K. Bou-Rabee. 2008
88 citations recorded by the source corpus.
Abstract We introduce the notion of quantifying the extent to which a finitely generated group is residually finite. We investigate this behavior for examples that include free groups, the first Grigorchuk group, finitely generated nilpotent groups, and certain arithmetic groups such as SL n ( Z ) . In the context of finite nilpotent quotients, we find a new characterization of finitely generated nilpotent groups.
Subfields: Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/37360c2b75c2fd4d50281da0e3ae7e91444793fa
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In Computational Theory and Mathematics
In Geometry and Topology
- Francesco Matucci
- Martin Kassabov
- Igor Rivin
- D. McReynolds
- Alexander Lubotzky
- Maryam Mirzakhani
- Richard Aoun
- Juan Souto
Citations in the corpus
- Bounding the residual finiteness of free groups (2009, methodology): “The following lemma of BouRabee [2] explains why the function FSG is independent on the generating set: Lemma 2.”
- Asymptotic growth and least common multiples in groups (2009, background): “2 and the upper bound of n(3) established in [1, 12] can be viewed as a weak Prime Number Theorem for free groups since the Prime Number Theorem yields F Z (n) ≈ log(n).”
- Geodesics with one self-intersection, and other stories (2009, background): “Khalid Bou-Rabee in [2] has analyzed the following question: given a residually finite group G and an element g ∈ G, how high an index subgroup H < G must one take so that g < H, in terms of the wordlength of g.”