Branch groups

By Laurent Bartholdi, Rostislav I. Grigorchuk, Zoran Sunik. 2005

217 citations recorded by the source corpus.

The class of branch groups is defined (both in the abstract and in the profinite category). The relationship of this class with the class of extremal groups is established. Properties of the branch groups are investigated. Applications of the congruence property to the theory of profinite branch groups are indicated. The weak maximality of parabolic subgroups in branch groups is proved.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7eb2f5cfad49774f109776fe60c3a24fc7548263

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In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

Groups of Intermediate Growth, an Introduction (2008, methodology): “We refer to extensive survey articles [1, 2, 6] and a recent”
Finite generation of iterated wreath products (2010, methodology): “tatement is obvious. For the converse we construct a ﬁnitely generated dense subgroup. The construction is based on the notions of directed automorphisms and branch groups introduced by R. Grigorchuk [5], and it is basically the same construction used by 1 P. Neumann [8], L. Bartholdi [1], D. Segal ”
On a series of finite automata defining free transformation groups (2006, background): “The formalization of these properties has resulted in the notions of a branch group (see [BGS]), a fractal group (see [BGN]), and, finally, the most general notion of a self-similar”
Asymptotic aspects of Schreier graphs and Hanoi Towers groups (2006, background): “A spherically transitive (transitive on all levels) group of tree automorphisms G is regularly branching over its subgroup is geometrically contained in K (meaning that the k factors act independently on the corresponding k subtrees of T rooted at the vertices of the ﬁrst level of T ; see [3]).”
Milnor's Problem on the Growth of Groups and its Consequences (2011, background): “Another important notion useful when studying growth is the notion of a branch group, introduced in [102, 103].”