ON RANK, ROOT AND EQUATIONS IN FREE GROUPS

DOI10.1142/S0218196701000565zbMath1026.20011MaRDI QIDQ4786286

Amnon Rosenmann

Publication date: 15 December 2002

Published in: International Journal of Algebra and Computation (Search for Journal in Brave)

zbMATH Keywords

rootsfinitely generated subgroupsfree groupsdirected graphssystems of equationsrank of subgroupsLyndon equation

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Free nonabelian groups (20E05)

Cites Work

• 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
• Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz
• Finite index and finite codimension
• Residual nilpotence and relations in free groups
• Some aspects of groups with unique roots
• On a Problem of Lyndon
• Products of powers in groups

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