Related papers: Dice periodic groups

We classify groups generated by powers of 2 Dehn twists which are 1) free or 2) have no ``unexpected'' reducible elements. We give some sufficient conditions in the case of groups generated by powers of more than two twists.

In order to induce a family of mixing patterns of leptons which accommodate the experimental data with a simple mathematical construct, we construct a novel object from the hybrid of two elements of a finite group with a parameter $\theta$.…

We introduce a new family of finite posets which we call 2-chains. These first arose in the study of 0-Hecke algebras, but they admit a variety of different characterisations. We give these characterisations, prove that they are equivalent…

A group is properly 3-realizable if it is the fundamental group of a compact polyhedron whose universal covering is proper homotopically equivalent to some 3-manifold. We prove that when such a group is also quasi-simply filtered then it…

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

We give the classification of elements - respectively cyclic subgroups - of finite order of the Cremona group, up to conjugation. Natural parametrisations of conjugacy classes, related to fixed curves of positive genus, are provided.

We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.

For a non-arithmetic Veech surface, it is known that the set points having finite orbit under the Veech group, called the set of periodic points, is finite. However, few examples of these periodic point sets have been computed. In what…

Given a prime power $p^d$ with $p$ a prime and $d$ a positive integer, we classify the finite groups $G$ with $p^{2d}$ dividing $|G|$ in which all subgroups of order $p^d$ are complemented and the finite groups $G$ having a normal…

The existence of an infinite simple boundedly generated 2-generated group and the existence of a boundedly simple 2-generated group containing a free non-cyclic subgroup are proved.

We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function.…

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

We produce an explicit family of totally real cyclic quartic polynomials that are monogenic in many cases and, if the $abc$ conjecture holds, generate distinct monogenic quartic fields infinitely often. Additional families (also…

We construct a 2-generated group $\Gamma $ such that its Cayley graph possesses finite connected subsets with arbitrarily big finite Heesch number.

We prove that the genus of a finite-dimensional division algebra is finite whenever the center is a finitely generated field of any characteristic. We also discuss potential applications of our method to other problems, including the…

The power graph of a group $G$ is a simple and undirected graph with vertex set $G$ and two distinct vertices are adjacent if one is a power of the other. In this article, we characterize (non-cyclic) finite groups of prime exponent and…

Over each nontrivial finite group $G$, there exists a finite system of equations having no solutions in larger finite groups but having a solution in a periodic group containing $G$. We prove several similar facts about amenable, orderable,…

By using the structure and some properties of extraspecial and generalized/almost extraspecial $p$-groups, we explicitly determine the number of elements of specific orders in such groups. As a consequence, one may find the number of cyclic…

We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.

We prove that every finitely-generated group of homeomorphisms of the 2-dimensional sphere all of whose elements have a finite order which is a power of 2 and so that there exists a uniform bound for the order of group elements is finite.…