Scott complexity and adjoining roots to finitely generated groups.

DOI10.4171/GGD/190zbMath1298.20033arXivmath/0612222OpenAlexW2023290983MaRDI QIDQ355389

Larsen Louder

Publication date: 24 July 2013

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612222

zbMATH Keywords

primitive elementsfinitely generated groupsfree productsfree groupsgraphs of groupsamalgamated productsgeometric group theoryindivisible elementsproper powers

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07) Free nonabelian groups (20E05) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Algebraic geometry over groups; equations over groups (20F70)

Related Items (9)

Negative immersions for one-relator groups ⋮ Magnus pairs in, and free conjugacy separability of, limit groups ⋮ The structure of limit groups over hyperbolic groups ⋮ On joins and intersections of subgroups in free groups ⋮ Krull dimension for limit groups. ⋮ One-ended subgroups of graphs of free groups with cyclic edge groups. ⋮ Word measures on symmetric groups ⋮ Twisting out fully irreducible automorphisms. ⋮ A Geometric Proof of the Structure Theorem for Cyclic Splittings of Free Groups

Cites Work

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• The equation \(a^2b^2=c^2\) in free groups
• The equation \(a^n b^n=c^n\) in a free group
• The equation \(a_ M=b^ Nc^ P\) in a free group
• Graphs of subgroups of free groups.
• Topology of finite graphs
• Residual nilpotence and relations in free groups
• A topological proof of Grushko's theorem on free products
• Finitely Generated 3-Manifold Groups are Finitely Presented
• Decomposition of a Group with a Single Defining Relation into a Free Product

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