Algebraic equivalents of the solvability of group-theoretic algorithmic problems

DOI10.1007/BF00971829zbMath0444.20030OpenAlexW2039184019MaRDI QIDQ1144654

Oleg V. Belegradek

Publication date: 1980

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00971829

zbMATH Keywords

finitely generated groupsfinitely presented groupssolvable word problemsolvable triviality problem

Mathematics Subject Classification ID

Applications of logic to group theory (20A15) Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Word problems, etc. in computability and recursion theory (03D40)

Cites Work

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• Recursive unsolvability of group theoretic problems
• The Boone-Higman theorem and the conjugacy problem
• On algebraically closed groups
• Subgroups of finitely presented groups
• An algebraic characterization of groups with soluble word problem
• Omitting quantifier-free types in generic structures
• An Embedding Theorem for Finitely Generated Groups

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