Growth of primitive elements in free groups

DOI10.1112/jlms/jdu009zbMath1308.20022arXiv1304.7979OpenAlexW3101681265MaRDI QIDQ2874650

Conan Wu, Doron Puder

Publication date: 8 August 2014

Published in: Journal of the London Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1304.7979

zbMATH Keywords

growth ratesprimitive elementsfree groupsword lengthsWhitehead algorithmrandom primitive words

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Asymptotic properties of groups (20F69) Free nonabelian groups (20E05) Asymptotic enumeration (05A16) Probabilistic methods in group theory (20P05)

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Average-case complexity of the Whitehead problem for free groups, Primitive and almost primitive elements of Schreier varieties, A note on the trace method for random regular graphs, The primitivity index function for a free group, and untangling closed curves on hyperbolic surfaces.With the appendix by Khalid Bou–Rabee, Expansion of random graphs: new proofs, new results, Measure preserving words are primitive

Cites Work

• Primitive words, free factors and measure preservation.
• Expansion of random graphs: new proofs, new results
• Automorphic orbits in free groups.
• A remark on `Counting primitive elements in free groups' (by J. Burillo and E. Ventura).
• Counting primitive elements in free groups
• On equivalent sets of elements in a free group
• Measure preserving words are primitive
• On Certain Sets of Elements in a Free Group
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