From automatic structures to automatic groups.

DOI10.4171/GGD/221zbMath1322.20025arXiv1107.3645OpenAlexW2962842353MaRDI QIDQ2016098

Bakhadyr Khoussainov, O. G. Kharlampovich, Alexei G. Myasnikov

Publication date: 19 June 2014

Published in: Groups, Geometry, and Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3645

zbMATH Keywords

Cayley graphsword problemfinitely generated nilpotent groupssolvable groupsCayley graph automatic groups

Mathematics Subject Classification ID

Generalizations of solvable and nilpotent groups (20F19) Geometric group theory (20F65) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10)

Related Items (24)

Thompson's group \(F\) is 1-counter graph automatic. ⋮ A combination theorem for affine tree-free groups ⋮ The inclusion structure of partially lossy queue monoids and their trace submonoids ⋮ Finitely Generated Semiautomatic Groups ⋮ On the geometry of Cayley automatic groups ⋮ Lamplighter groups and automata ⋮ Metric properties of Baumslag–Solitar groups ⋮ Higher rank lamplighter groups are graph automatic ⋮ Algorithms and topology of Cayley graphs for groups. ⋮ String compression in FA-presentable structures ⋮ Semiautomatic structures ⋮ The monoid of queue actions ⋮ Geometry of the word problem for 3-manifold groups ⋮ Tree languages and branched groups ⋮ The complexity of verbal languages over groups ⋮ Quasi-automatic semigroups ⋮ Unnamed Item ⋮ Dynamic algorithms for multimachine interval scheduling through analysis of idle intervals ⋮ AUTOMATIC AND POLYNOMIAL-TIME ALGEBRAIC STRUCTURES ⋮ Cayley Automatic Groups and Numerical Characteristics of Turing Transducers ⋮ FOUNDATIONS OF ONLINE STRUCTURE THEORY ⋮ Cayley polynomial-time computable groups ⋮ BEING CAYLEY AUTOMATIC IS CLOSED UNDER TAKING WREATH PRODUCT WITH VIRTUALLY CYCLIC GROUPS ⋮ An example of an automatic graph of intermediate growth

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