Related papers: Dice periodic groups

In this note, we investigate how different fundamental groups of presentations of a fixed algebra $A$ can be. For finitely many finitely presented groups $G_i$, we construct an algebra $A$ such that all $G_i$ appear as fundamental groups of…

We give an elementary construction of polyhedra whose links are connected bipartite graphs, which are not necessarily isomorphic pairwise. We show, that the fundamental groups of some of our polyhedra contain surface groups. In particular,…

We study the algebras generated by restriction and induction operations on complex modules over dihedral groups. In the case where the orders of all dihedral groups involved are not divisible by four, we describe the relations, a basis, the…

We prove that any finitely generated one ended group has linear end depth. Moreover, we give alternative proofs to theorems relating the growth of a finitely generated group to the number of its ends.

An l-group G is an abelian group equipped with a translation invariant lattice order. Baker and Beynon proved that G is finitely generated projective iff it is finitely presented. A unital l-group is an l-group G with a distinguished order…

Answering a question of Dan Haran and generalizing some results of Aschbacher-Guralnick and Suzuki, we prove that given a set of primes pi, any finite group can be generated by a pi-subgroup and a pi'-subgroup. This gives a free product…

Given an initial family of sets, we may take unions, intersections and complements of the sets contained in this family in order to form a new collection of sets; our construction process is done recursively until we obtain the last family.…

A 2-covering for a finite group $G$ is a set of proper subgroups of $G$ such that every pair of elements of $G$ is contained in at least one subgroup in the set. The minimal number of subgroups needed to 2-cover a group $G$ is called the…

The finite groups having an indecomposable polynomial invariant whose degree is at least half of the order of the group are classified. Apart from four sporadic exceptions these are exactly the groups having a cyclic subgroup of index at…

In 1934, Garrett Birkhoff has shown that the number of isomorphism classes of finite metabelian groups of order $p^{22}$ tends to infinity with $p$. More precisely, for each prime number $p$ there is a family…

We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…

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…

Let $d$ be a positive integer. A finite group is called $d$-maximal if it can be generated by precisely $d$ elements, while its proper subgroups have smaller generating sets. For $d\in\{1,2\}$, the $d$-maximal groups have been classified up…

We introduce the depth parameters of a finite semigroup, which measure how hard it is to produce an element in the minimum ideal when we consider generating sets satisfying some minimality conditions. We estimate such parameters for some…

Consider the power pseudorandom-number generator in a finite field ${\mathbb F}_q$. That is, for some integer $e\ge2$, one considers the sequence $u,u^e,u^{e^2},\dots$ in ${\mathbb F}_q$ for a given seed $u\in {\mathbb F}_q^\times$. This…

A finitely generated solvable group with unbounded iterated identity is constructed.

We exhibit infinite, solvable, virtually abelian groups with a fixed number of generators, having arbitrarily large balls consisting of torsion elements. We also provide a sequence of 3-generator non-virtually nilpotent polycyclic groups of…

In this paper we obtain significant bounds for the number of maximal subgroups of a given index of a finite group. These results allow us to give new bounds for the number of random generators needed to generate a finite $d$-generated group…

We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given finite metacyclic groups are isomorphic, and another algorithm…

We compute the fundamental groups of the complements of the family of real conic-line arrangements with up to two conics which are tangent to each other at two points, with an arbitrary number of tangent lines to both conics. All the…