Just Infinite Branch Groups

By Rostislav I. Grigorchuk. 2000

231 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/782a5f68b45f8964c8fe112d5e988498829ed7f7

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In Computational Theory and Mathematics

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Classification of groups generated by 3-state automata over a 2-letter alphabet (2008, methodology): “More on the class of branch group can be found in [ Gri00 ] and [BGˇ”
GGS-groups: Order of congruence quotients and Hausdorff dimension (2011, background): “We have ψ(b) = (a, b), and then by direct calculation ψ((ab)(2)) = (ba, ab) (see also Section 6 of [11]).”
Dimension and randomness in groups acting on rooted trees (2002, methodology): “By the characterization of Grigorchuk (2000) (which is based on Wilson (1971)), groups with this property fall into two classes: one is the so-called branch groups, which have a natural action on T (p) (see Section 9 for details).”
Simple locally compact groups acting on trees and their germs of automorphisms (2010, background): “(iii) It is possible to dene branch groups without explicitly referring to the associated rooted tree; see, for example, [ Gri00 , Sect.”
CUNTZ-PIMSNER ALGEBRAS OF GROUP ACTIONS (2004, methodology): “It has other interesting properties such as just-infiniteness and finite width (see [ 15 ]).”
ON THE WORD AND PERIOD GROWTH OF SOME GROUPS OF TREE AUTOMORPHISMS (2000, background): “See [3] for definitions and for more constructions of groups of similar flavor.”
Milnor's Problem on the Growth of Groups and its Consequences (2011, methodology): “With each sequence m̄ = {mn}n=1 consisting of integers mn ≥ 2, one can associate a spherically homogeneous rooted tree Tm̄ as done in [27, 103, 22].”
Group Laws and Free Subgroups in Topological Groups (2003, result): “The above result generalises a result of Wilson [ Wi2 ] who proved that for branch profinite groups the subset of n-tuples in G n generating non-free subgroups is meagre (first category) in G n . His result implies that finitely generated”