Related papers: On Conditions Relating to Nonsolvability

The Thompson group $V$, as well as the Brin-Thompson group $2V$, is finitely generated and can be defined as a monoid acting on bitstrings, respectively pairs of bitstrings. Therefore evaluation problems can be defined for $V$ and $2V$. We…

Let $F$ denote the Thompson group with standard generators $A=x_0$, $B=x_1$. It is a long standing open problem whether $F$ is an amenable group. By a result of Kesten from 1959, amenability of $F$ is equivalent to $$(i)\qquad ||I+A+B||=3$$…

The structure of groups for which certain sets of commutator subgroups are finite is investigated, with a particular focus on the relationship between these groups and those with finite derived subgroup.

Let $p$ be an odd prime and let $\mathcal{F}$ be a fusion system over a finite $p$-group $P$. A fusion system $\mathcal{F}$ is said to be nilpotent if $\mathcal{F}=\mathcal{F}_{P}(P)$. In this paper we provide new criteria for saturated…

A general separability condition on the second moment (covariance matrix) for continuous variable two-party systems is derived by an analysis analogous to the derivation of the Kennard's uncertainty relation without referring to the…

Stackability for finitely presented groups consists of a dynamical system that iteratively moves paths into a maximal tree in the Cayley graph. Combining with formal language theoretic restrictions yields auto- or algorithmic stackability,…

Let $G$ be a finite group. In this short note, we give a criterion of nilpotency of $G$ based on the existence of elements of certain order in each section of $G$.

In this paper, for the first time in the literature, we study the stability of solutions of two classes of feasibility (i.e., split equality and split feasibility) problems by set-valued and variational analysis techniques. Our idea is to…

Let $PL_0(I)$ represent the group of orientation-preserving piecewise-linear homeomorphisms of the unit interval which admit finitely many breaks in slope, under the operation of composition. We find a non-solvable group $W$ and show that…

Bouc proposed the following conjecture: a finite group $G$ is nilpotent if and only if its largest quotient $B$-group $\beta(G)$ is nilpotent. And he has prove that this conjecture holds when $G$ is solvable. In this paper, we consider the…

This paper addresses a decision problem highlighted by Grigorchuk, Nekrashevich, and Sushchanskii, namely the finiteness problem for automaton (semi)groups. For semigroups, we give an effective sufficient but not necessary condition for…

Classification problems have been introduced by M. Ziegler as a generalization of promise problems. In this paper we are concerned with solvability and unsolvability questions with respect to a given set or language family, especially with…

Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…

Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…

We prove that in an arbitrary semigroup without cycles, the problem of divisibility and, therefore, the word problem is solvable.

We consider the group testing problem, in the case where the items are defective independently but with non-constant probability. We introduce and analyse an algorithm to solve this problem by grouping items together appropriately. We give…

In this paper, we consider solvable groups that satisfy the two-prime hypothesis. We prove that if $G$ is such a group and $G$ has no nonabelian nilpotent quotients, then $|\cd G| \le 462,515$. Combining this result with the result from…

We study a conjecture by Deaconescu on the solubility of finite groups with claims that if more than half of the elements in a finite group has the same order $k$, then the group is soluble. We show that the original conjecture fails by…

We apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed…

It is shown that finite groups in which the order of the product of every pair of elements of co-prime order is the product of the orders, is nilpotent.