FINITE INDEX SUBGROUPS OF FULLY RESIDUALLY FREE GROUPS

DOI10.1142/S0218196711006388zbMath1253.20024arXiv0809.0938MaRDI QIDQ3013894

D. E. Serbin, Andrey V. Nikolaev

Publication date: 19 July 2011

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

Full work available at URL: https://arxiv.org/abs/0809.0938

zbMATH Keywords

algorithmssubgroups of finite indexlimit groupsfinitely generated fully residually free groupsGreenberg-Stallings theorem

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Residual properties and generalizations; residually finite groups (20E26)

Related Items

Groups with free regular length functions in $\mathbb{Z}^{n}$, Ascending chains of finitely generated subgroups, Green index in semigroups: generators, presentations, and automatic structures., Limit groups over coherent right-angled Artin groups, Membership problem in groups acting freely on \(\mathbb N^n\)-trees., Subgroup properties of pro-\(p\) extensions of centralizers., ACTIONS, LENGTH FUNCTIONS, AND NON-ARCHIMEDEAN WORDS, A list of applications of Stallings automata, Detecting conjugacy stability of subgroups in certain classes of groups

Cites Work

• The isomorphism problem for finitely generated fully residually free groups.
• Normalisers in limit groups.
• Topology of finite graphs
• Algebraic geometry over groups. I: Algebraic sets and ideal theory
• Irreducible affine varieties over a free group. I: Irreducibility of quadratic equations and Nullstellensatz
• Irreducible affine varieties over a free group. II: Systems in triangular quasi-quadratic form and description of residually free groups
• Combination of convergence groups.
• Stallings foldings and subgroups of free groups
• Diophantine geometry over groups. II: Completions, closures and formal solutions
• Diophantine geometry over groups. I: Makanin-Razborov diagrams
• EXPONENTIAL GROUPS 2: EXTENSIONS OF CENTRALIZERS AND TENSOR COMPLETION OF CSA-GROUPS
• FULLY RESIDUALLY FREE GROUPS AND GRAPHS LABELED BY INFINITE WORDS