Automatically presented groups.

DOI10.4171/GGD/3zbMath1183.20040MaRDI QIDQ2372588

A. G. Erschler

Publication date: 31 July 2007

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

zbMATH Keywords

word problemnilpotent groupsamenabilityfinitely presented groupspolycyclic groupsHaagerup propertyproperty \(T\)Cayley topologyGrigorchuk topologygroups generated by finite state automatapiecewise automatically presented groups

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Topological methods in group theory (57M07) Asymptotic properties of groups (20F69) Word problems, other decision problems, connections with logic and automata (group-theoretic aspects) (20F10) Groups acting on trees (20E08) Means on groups, semigroups, etc.; amenable groups (43A07)

Related Items (6)

The classification of abelian groups generated by time-varying automata and by Mealy automata over the binary alphabet ⋮ The concept of self-similar automata over a changing alphabet and lamplighter groups generated by such automata ⋮ The concept of duality for automata over a changing alphabet and generation of a free group by such automata ⋮ On some universal construction of minimal topological generating sets for inverse limits of iterated wreath products of non-abelian finite simple groups ⋮ Amenable groups without finitely presented amenable covers ⋮ A group of non-uniform exponential growth locally isomorphic to $IMG(z^2+i)$

Cites Work

• Endomorphic presentations of branch groups.
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