Groups with Context-free Co-word Problem and Embeddings into Thompson’s Group V

Berns-Zieve, Rose; Fry, Dana; Gillings, Johnny; Hoganson, Hannah; Mathews, Heather

doi:10.1017/9781108526203.003

Cited by 3 publications

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Groups, Languages and Automata

Holt

Rees

Röver

2017

View full text Add to dashboard Cite

Fascinating connections exist between group theory and automata theory, and a wide variety of them are discussed in this text. Automata can be used in group theory to encode complexity, to represent aspects of underlying geometry on a space on which a group acts, and to provide efficient algorithms for practical computation. There are also many applications in geometric group theory. The authors provide background material in each of these related areas, as well as exploring the connections along a number of strands that lead to the forefront of current research in geometric group theory. Examples studied in detail include hyperbolic groups, Euclidean groups, braid groups, Coxeter groups, Artin groups, and automata groups such as the Grigorchuk group. This book will be a convenient reference point for established mathematicians who need to understand background material for applications, and can serve as a textbook for research students in (geometric) group theory.

show abstract

Groups, Languages and Automata

Holt

Rees

Röver

2017

View full text Add to dashboard Cite

show abstract

Braiding groups of automorphisms and almost-automorphisms of trees

Skipper¹,

Zaremsky²

2023

Can. J. Math.-J. Can. Math.

View full text Add to dashboard Cite

We introduce "braided" versions of self-similar groups and Röver-Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu, who considered the case when the self-similar groups are what we call "self-identical". In particular we use a braided version of the Grigorchuk group to construct a new group called the braided Röver group, which we prove is of type F ∞ . Our techniques involve using so called -ary cloning systems to construct the groups, and analyzing certain complexes of embedded disks in a surface to understand their finiteness properties.

show abstract

Thompson groups for systems of groups, and their finiteness properties

Witzel

Zaremsky

2018

Groups Geom. Dyn.

View full text Add to dashboard Cite

We describe a procedure for constructing a generalized Thompson group out of a family of groups that is equipped with what we call a cloning system. The previously known Thompson groups F , V , V br and F br arise from this procedure using, respectively, the systems of trivial groups, symmetric groups, braid groups and pure braid groups.We give new examples of families of groups that admit a cloning system and study how the finiteness properties of the resulting generalized Thompson group depend on those of the original groups. The main new examples here include upper triangular matrix groups, mock reflection groups, and loop braid groups. For generalized Thompson groups of upper triangular matrix groups over rings of S-integers of global function fields, we develop new methods for (dis-)proving finiteness properties, and show that the finiteness length of the generalized Thompson group is exactly the limit inferior of the finiteness lengths of the groups in the family.

show abstract

Groups with Context-free Co-word Problem and Embeddings into Thompson’s Group V

Cited by 3 publications

References 7 publications

Groups, Languages and Automata

Groups, Languages and Automata

Braiding groups of automorphisms and almost-automorphisms of trees

Thompson groups for systems of groups, and their finiteness properties

Contact Info

Product

Resources

About