A. Smoktunowicz and L. Vendramin conjectured that if A is a finite skew brace with solvable additive group, then the multiplicative group of solvable. In this short note we make step towards positive solution conjecture proving minimal non-solvable not simple. On way to obtaining result, prove correct in case when order divisible by 3.

Time series are composed of sequences of data items measured at typically uniform intervals. Time series arise frequently in many scientific and engineering applications, including finance, medicine, digital audio, and motion capture. Time series motifs are repeated similar subseries in one or multiple time series data. Time series anomalies are unusual subseries in one or multiple time series ...

‎Let $G$ be a finite group‎. ‎We say that the derived covering number of $G$ is finite if and only if there exists a positive integer $n$ such that $C^n=G'$ for all non-central conjugacy classes $C$ of $G$‎. ‎In this paper we characterize solvable groups $G$ in which the derived covering number is finite‎.‎ 

Several explicit examples of multi-particle quasi exactly solvable ‘discrete’ quantum mechanical Hamiltonians are derived by deforming the well-known exactly solvable multi-particle Hamiltonians, the Ruijsenaars-Schneider-van Diejen systems. These are difference analogues of the quasi exactly solvable multi-particle systems, the quantum Inozemtsev systems obtained by deforming the well-known ex...

Let PL0(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 groupW and show thatW embeds in every non-solvable subgroup of PL0(I). We find mild conditions under which other non-solvable subgroups (B, (≀Z≀), (Z≀), and (≀Z)) embed in subgroups of ...

It is shown that any non-solvable Latin Tableau (LT) has a solvable LT-extension with the same shape, and an algorithm computing the minimal such extension is presented. Minimal Latin Square embeddings of solvable Latin Tableaux are established. The results depend partly on the truth of the Wide Partition Conjecture for Latin Tableaux. More about Latin Tableaux and their Embeddings Bart Demoen ...

In this paper, first we introduce the notions of k-nilpotent (solvable) ideals and BCK-algebras. Specially, show that every commutative ideal is 1-nilpotent (solvable). Second, state an equivalent condition to k-nilpotency (solvablity) BCK-algebra. Finally, study n-fold 2-nilpotent BCK-algebras as a generalization BCK-algebras, relation between these two concepts. Basically, compare solvable (B...

We prove that an element g of prime order > 3 belongs to the solvable radical R(G) of a finite (or, more generally, a linear) group if and only if for every x ∈ G the subgroup generated by g, xgx is solvable. This theorem implies that a finite (or a linear) group G is solvable if and only if in each conjugacy class of G every two elements generate a solvable subgroup.