Bounding the residual finiteness of free groups

By Martin Kassabov, Francesco Matucci. 2009

47 citations recorded by the source corpus.

We find a lower bound to the size of finite groups detecting a given word in the free group, more precisely we construct a word wn of length n in non-abelian free groups with the property that wn is the identity on all finite quotients of size ? n2/3 or less. This improves on a previous result of Bou- Rabee and McReynolds quantifying the lower bound of the residual finiteness of free groups.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/f2704f070d0e5917ec08edc321876bc1ad37859c

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In Computational Theory and Mathematics

1. D. McReynolds
2. Francesco Matucci
3. Martin Kassabov

In Geometry and Topology

1. D. McReynolds
2. Francesco Matucci
3. Martin Kassabov

Citations in the corpus

• Asymptotic growth and least common multiples in groups (2009, background): “We refer the reader to [7] for additional questions and conjectures.”