On asymptotic properties of verbal subsets in a group.

DOI10.1134/S1995080215040113zbMath1338.20028OpenAlexW2298210374MaRDI QIDQ266232

Alexei G. Myasnikov, Vitaliĭ Roman'kov

Publication date: 13 April 2016

Published in: Lobachevskii Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1995080215040113

zbMATH Keywords

free groupsdefinable subsetsasymptotic densitiesverbal subsets

Mathematics Subject Classification ID

Asymptotic properties of groups (20F69) Free nonabelian groups (20E05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Cites Work

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• Quasimorphisms and laws.
• Word maps, conjugacy classes, and a noncommutative Waring-type theorem.
• The Ore conjecture.
• scl.
• Width of verbal subgroups in solvable groups
• Volume and bounded cohomology
• Cohomological lower bounds for isoperimetric functions on groups
• On rationality of verbal subsets in a group
• The Complexity of Verbal Languages over Groups
• Word maps and Waring type problems
• ON THE PARAMETERIZATION OF SOLUTIONS FOR EQUATIONS IN FREE GROUPS
• PRODUCTS OF COMMUTATORS AND PRODUCTS OF SQUARES IN A FREE GROUP
• Products of Commutators in Free Products
• On the number of nonorientable Wicks forms in a free group
• DEFINABLE SETS IN A HYPERBOLIC GROUP
• Some Remarks on Commutators