Deciding if an automorphism of an infinite soluble group is inner

DOI10.1017/S0017089500009344zbMath0711.20021MaRDI QIDQ3496403

Derek J. S. Robinson

Publication date: 1990

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

zbMATH Keywords

relationswordsalgorithmsautomorphismgeneratorsendomorphismfinitely generated metabelian groupsouter automorphism groupalgorithmic problemssoluble word problemrecursively undecidablefinitely generated recursive presentationnilpotent-by-polycyclic-by-finite groupsoluble-by-finite group of finite Prüfer rank

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Solvable groups, supersolvable groups (20F16) Generators, relations, and presentations of groups (20F05) Automorphisms of infinite groups (20E36) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Software, source code, etc. for problems pertaining to group theory (20-04)

Cites Work

• Algorithmically insoluble problems about finitely presented solvable groups, Lie and associative algebras. I
• Some recognizable properties of solvable groups
• Computable algebra and group embeddings
• Infinitely generated subgroups of finitely presented groups. I
• Constructable solvable groups
• The Word Problem for Finitely Generated Soluble Groups of Finite Rank
• A Finitely Presented Group Whose Group of Automorphisms is Infinitely Generated

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