On rational and concise words.

DOI10.1016/J.JALGEBRA.2015.02.003zbMath1346.20042arXiv1406.7175OpenAlexW2963839379MaRDI QIDQ2341308

P. V. Shumyatskij, Robert M. Guralnick

Publication date: 24 April 2015

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1406.7175

zbMATH Keywords

commutatorsresidually finite groupsequations over groupsmultilinear commutator wordsverbal subgroupsgroup wordssolutions of equationsconcise wordsweakly rational words

Mathematics Subject Classification ID

Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Residual properties and generalizations; residually finite groups (20E26) Commutator calculus (20F12) Algebraic geometry over groups; equations over groups (20F70)

Related Items (18)

Commutators, centralizers, and strong conciseness in profinite groups ⋮ Strong conciseness of coprime commutators in profinite groups ⋮ On conciseness of the word in Olshanskii's example ⋮ On bounded conciseness of words in residually finite groups ⋮ Bounding the order of a verbal subgroup in a residually finite group ⋮ On conciseness of some commutator words ⋮ Groups with boundedly many commutators of maximal order ⋮ Unnamed Item ⋮ Word problems for finite nilpotent groups ⋮ On bounded conciseness of Engel-like words in residually finite groups ⋮ On finiteness of some verbal subgroups in profinite groups ⋮ On profinite groups with Engel-like conditions. ⋮ Engel groups in bath - ten years later ⋮ Words of Engel type are concise in residually finite groups. II. ⋮ Strong conciseness in profinite groups ⋮ Geometry of word equations in simple algebraic groups over special fields ⋮ Words of Engel type are concise in residually finite groups ⋮ On conciseness of words in profinite groups.

Cites Work

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• On words that are concise in residually finite groups.
• Omega subgroups of pro-\(p\) groups.
• WORDS WITH FEW VALUES IN FINITE SIMPLE GROUPS
• Outer commutator words are uniformly concise
• IMAGES OF WORD MAPS IN FINITE SIMPLE GROUPS
• Finiteness Conditions for Verbal Subgroups
• On Outer-Commutator Words

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