POLYCYCLIC, METABELIAN OR SOLUBLE OF TYPE (FP)∞ GROUPS WITH BOOLEAN ALGEBRA OF RATIONAL SETS AND BIAUTOMATIC SOLUBLE GROUPS ARE VIRTUALLY ABELIAN

DOI10.1017/S0017089516000677zbMath1427.20041arXiv1511.00223OpenAlexW2257646946MaRDI QIDQ4600319

Vitaliĭ Roman'kov

Publication date: 8 January 2018

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

Full work available at URL: https://arxiv.org/abs/1511.00223

Mathematics Subject Classification ID

Formal languages and automata (68Q45) Solvable groups, supersolvable groups (20F16) Geometric group theory (20F65) Homological methods in group theory (20J05) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Structure theory of Boolean algebras (06E05)

Related Items (4)

The Development of the Theory of Automatic Groups ⋮ Superpositions of free Fox derivations ⋮ Undecidability of the submonoid membership problem for free nilpotent group of class $l\geqslant 2$ of sufficiently large rank ⋮ Two problems for solvable and nilpotent groups

Cites Work

• Intersections of finitely generated subgroups in metabelian groups
• Rational subgroups of biautomatic groups
• On groups of type \((FP)_\infty\)
• Soluble Groups of Type (FP)∞ have Finite Torsion-Free Rank
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