相关论文: Branch Groups

These lecture notes provide an introduction to automorphism groups of graphs. Some special families of graphs are then discussed, especially the families of Cayley graphs generated by transposition sets.

This is the first one in a series of papers classifying the factorizations of almost simple groups with nonsolvable factors. In this paper we deal with almost simple linear groups.

In this work, we give a survey of recent developments in the theory of partial actions of groups and Hopf algebras.

We give presentations of braid groups and pure braid groups on surfaces.

This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…

A transitive permutation group is semiprimitive if each of its normal subgroups is transitive or semiregular. Interest in this class of groups is motivated by two sources: problems arising in universal algebra related to collapsing monoids…

In many real network systems, nodes usually cooperate with each other and form groups, in order to enhance their robustness to risks. This motivates us to study a new type of percolation, group percolation, in interdependent networks under…

In this paper we give a description of the generators of the prime level congruence subgroups of braid groups. Also, we give a new presentation of the symplectic group over a finite field, and we calculate symmetric quotients of the prime…

Rooted, weighted continuum random trees are used to describe limits of sequences of random discrete trees. Formally, they are random quadruples $(\mathcal{T},d,r,p)$, where $(\mathcal{T},d)$ is a tree-like metric space, $r\in\mathcal{T}$ is…

Network visualization allows a quick glance at how nodes (or actors) are connected by edges (or ties). A conventional network diagram of "contact tree" maps out a root and branches that represent the structure of nodes and edges, often…

The theory of Hubbard trees provides an effective classification of non-linear post-critically finite polynomial maps from \C to itself. This note will extend this classification to the case of maps from a finite union of copies of \C to…

In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.

This paper makes some preliminary observations towards an extension of current work on graphs defined on groups to simplicial complexes. I define a variety of simplicial complexes on a group which are preserved by automorphisms of the…

We study constructions of groups, in particular of groups of intermediate rank, which are accessible to surgery techniques.

In this paper we study the adjacency spectrum of families of finite rooted trees with regular branching properties. In particular, we show that in the case of constant branching, the eigenvalues are realized as the roots of a family of…

A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a 'Tree of Life.' In this paper we use an…

We apply the theory of branches in Bruhat-Tits trees, developed in previous works by the second author and others, to the study of two dimensional representations of finite groups over the ring of integers of a number field. We provide a…

The character theory of finite groups has numerous basic questions that are often already quite involved: enumerating of irreducible characters, their character formulas, point-wise product decompositions, and restriction/induction between…

We give closed form expressions for the numbers of multi-rooted plane trees with specified degrees of root vertices. This results in an infinite number of integer sequences some of which are known to have an alternative interpretation. We…

Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…