Some recognizable properties of solvable groups

DOI10.1007/BF01214868zbMath0455.20027OpenAlexW2029675586MaRDI QIDQ1150042

Gilbert Baumslag, Charles F. III Miller, Frank B. Cannonito

Publication date: 1981

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/173102

zbMATH Keywords

word problemfinitely presented solvable groupalgorithmically recognizable propertiesintegral group ring of a polycyclic groupnilpotent-by-polycyclic groups

Mathematics Subject Classification ID

Solvable groups, supersolvable groups (20F16) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Generators, relations, and presentations of groups (20F05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (8)

Recursive categoricity and recursive stability ⋮ Some algorithmic problems for relatively free groups ⋮ Deciding if an automorphism of an infinite soluble group is inner ⋮ Implementing the Baumslag-Cannonito-Miller polycyclic quotient algorithm ⋮ The algorithmic theory of polycyclic-by-finite groups ⋮ Verifying nilpotence ⋮ Model-theoretic and algorithmic questions in group theory ⋮ Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. II

Cites Work

• Recursive unsolvability of group theoretic problems
• A note on normal and nonnormal subgroups of given index
• Computable algebra and group embeddings

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