Related papers: A problem in comparative order theory

Let $p$ be a prime and $G$ a subgroup of $GL_d(p)$. We define $G$ to be $p$-exceptional if it has order divisible by $p$, but all its orbits on vectors have size coprime to $p$. We obtain a classification of $p$-exceptional linear groups.…

We will describe an algorithm to arrange all the positive and negative integer numbers. This array of numbers permits grouping them in six different Classes, $\alpha$, $\beta$, $\gamma$, $\delta$, $\epsilon$, and $\zeta$. Particularly,…

A poset $\bfp$ is well-partially ordered (WPO) if all its linear extensions are well orders~; the supremum of ordered types of these linear extensions is the {\em length}, $\ell(\bfp)$ of $\bfp$. We prove that if the vertex set $X$ of…

The class of abelian $p$-groups are an example of some very interesting phenomena in computable structure theory. We will give an elementary first-order theory $T_p$ whose models are each bi-interpretable with the disjoint union of an…

Let $p$ be a prime and let $K$ be a finite extension of the field ${\bf Q}_p$ of $p$-adic numbers such that the group ${}_pK^\times$ has order $p$. The ${\bf F}_p$-space $K^\times\!/K^{\times p}$ carries a natural filtration coming from the…

In finite problems comprising objects, situations, and an object- and situation-contingent payoff function, we study the comparative statics of the set of undominated objects, meaning those for which there exists no mixture over objects…

In this paper we study the finite groups in which every element has prime power order, briefly them EPPO-groups. The classification of EPPO-groups is given including the cases of solvable, non-solvable and simple EPPO-groups. This paper is…

In the ordinal Matroid Secretary Problem (MSP), elements from a weighted matroid are presented in random order to an algorithm that must incrementally select a large weight independent set. However, the algorithm can only compare pairs of…

Given a finite set $X$ and an ordering $\succeq$ over its subsets, the $l$-out-of-$d$ maximin-share of $X$ is the maximal (by $\succeq$) subset of $X$ that can be constructed by partitioning $X$ into $d$ parts and picking the worst union of…

We consider the families of finite Abelian groups $\ZZ/p\ZZ\times \ZZ/p\ZZ$, $\ZZ/p^2\ZZ$ and $\ZZ/p\ZZ\times \ZZ/q\ZZ$ for $p,q$ two distinct prime numbers. For the two first families we give a simple characterization of all functions…

The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…

Many computational problems can be modelled as the class of all finite structures $\mathbb A$ that satisfy a fixed first-order sentence $\phi$ hereditarily, i.e., we require that every (induced) substructure of $\mathbb A$ satisfies $\phi$.…

The article deals with finite groups in which commutators have prime power order (CPPO-groups). We show that if G is a soluble CPPO-group, then the order of the commutator subgroup G' is divisible by at most two primes.

Given a power $q$ of a prime number $p$ and "nice" polynomials $f_1,...,f_r\in\bbF_q[T,X]$ with $r=1$ if $p=2$, we establish an asymptotic formula for the number of pairs $(a_1,a_2)\in\bbF_q^2$ such that…

The structure of finite and locally finite groups in which every element has prime power order (CP-groups) is well known. In this paper we note that the combination of our earlier results with the available information on the structure of…

Complex networks are everywhere. They appear for example in the form of biological networks, social networks, or computer networks and have been studied extensively. Efficient algorithms to solve problems on complex networks play a central…

We investigate the occurrence of elements of order $p$ in the upper central series of a finite $p$-group.

We prove that there is no fpt-algorithm that can approximate the dominating set problem with any constant ratio, unless FPT= W[1]. Our hardness reduction is built on the second author's recent W[1]-hardness proof of the biclique problem.…

Let $X$ be a scheme of finite type over $\mathbf{Z}$. For $p \in \mathcal{P}$ the set of prime numbers, let $N_{X}(p)$ be the number of $\mathbf{F}_{p}$-points of $X/\mathbf{F}_{p}$. For fixed $n\geq 1$ and $a_{1}, \ldots, a_{n} \in…

We characterise the classes of tournaments with tractable first-order model checking. For every hereditary class of tournaments $\mathcal T$, first-order model checking is either fixed parameter tractable or $\textrm{AW}[*]$-hard. This…