Related papers: Branch groups with infinite rigid kernel

We introduce the notion of graphical discreteness to group theory. A finitely generated group is graphically discrete if whenever it acts geometrically on a locally finite graph, the automorphism group of the graph is compact-by-discrete.…

A major difficult problem in Galois theory is the characterization of profinite groups which are realizable as absolute Galois groups of fields. Recently the Kernel $n$-Unipotent Conjecture and the Vanishing $n$-Massey Conjecture for $n\geq…

We prove a finiteness theorem for subgroups of bounded rank in hyperbolic $3$-manifold groups. As a consequence, we show that every bounded rank covering tower of closed hyperbolic $3$-manifolds is a tower of finite covers associated to a…

We describe the infinite dihedral group as automaton group. We collect basic results and give full proofs in details for all statements.

In \cite{Kramer11} Kramer proves for a large class of semisimple Lie groups that they admit just one locally compact $\sigma$-compact Hausdorff topology compatible with the group operations. We present two different methods of generalising…

We restructure and advance the classification theory of finite racks and quandles by employing powerful methods from transformation groups and representation theory, especially Burnside rings. These rings serve as universal receptacles for…

We show that a hyperbolic $3$-manifold can be the cyclic branched cover of at most fifteen knots in $\mathbf{S}^3$. This is a consequence of a general result about finite groups of orientation preserving diffeomorphisms acting on…

Let $C_{k_1}, \ldots, C_{k_n}$ be cycles with $k_i\geq 2$ vertices ($1\le i\le n$). By attaching these $n$ cycles together in a linear order, we obtain a graph called a polygon chain. By attaching these $n$ cycles together in a cyclic…

In this article we construct a series of new infinite families of strongly regular graphs with the same parameters as the point-graphs of non-singular quadrics in PG(n,2).

The Directed Power Graph of a group is a graph whose vertex set is the elements of the group, with an edge from $x$ to $y$ if $y$ is a power of $x$. The \textit{Power Graph} of a group can be obtained from the directed power graph by…

We prove a topological rigidity result for simple, thick, hyperbolic P-manifolds of dimension 2: isomorphism of the fundamental groups implies homeomorphism of the P-manifolds. An immediate application is a diagram rigidity theorem for…

The critical group of a graph is a finite abelian group whose order is the number of spanning forests of the graph. This paper provides three basic structural results on the critical group of a line graph. The first deals with connected…

In this article, we study the properties of profinite geometric iterated monodromy groups associated to polynomials. Such groups can be seen as generic representations of absolute Galois groups of number fields into the automorphism group…

The Birman exact sequence describes the effect on the mapping class group of a surface with boundary of gluing discs to the boundary components. We construct an analogous exact sequence for the automorphism group of a free group. For the…

We prove the dichotomy that every Coxeter group either has a strongly solid group von Neumann algebra or contains the product of an infinite cyclic group and a free group of rank 2. This generalizes the same dichotomy for right-angled…

We study the connectivity of proper power graphs of some family of finite groups including nilpotent groups, groups with a non-trivial partition, and symmetric and alternating groups.

The notion of a flag kernel on a homogeneous group is exteded to distributions of arbitrary multidimensional order. It is shown that under natural restrictions on order the operation of convolution admits an extension to thus generalised…

The tensor powers of the vector representation associated to an infinite rank quantum group decompose into irreducible components with multiplicities independant of the infinite root system considered. Although the irreducible modules…

We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of…

This is Chapter 24 in the "AutoMathA" handbook. Finite automata have been used effectively in recent years to define infinite groups. The two main lines of research have as their most representative objects the class of automatic groups…