Let k0 be a finite algebraic number field in a fixed algebraic closure Ω and ζn denote a primitive n-th root of unity ( n ≥ 1). Let k∞ be the maximal cyclotomic extension of k0, i.e. the field obtained by adjoining to k0 all ζn ( n = 1, 2, ...). Let M and L be the maximal abelian extension of k∞ and the maximal unramified abelian extension of k∞ respectively. The Galois groups Gal(M/k∞) and Gal...

Fischer, Lynch and Paterson showed in a fundamental paper that achieving a distributed agreement for N > 1 processors is impossible in the presence of ohe faulty processor. This' resulf was hiter extended by Wolfstahl and Moran who showed that it holdS for any task with a connected input graph and a ~connected decision graph (where a vertex in the input [decision] graph is an N -tuple of input ...

‎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...

Let G = {G1; G2; : : : ; Gn; : : :} be a sequence of graphs with Gn having n vertices and having a random distribution of t(n) pebbles to its vertices. If s¿ 2 is an integer, the event that Gn has s or more vertices with two or more pebbles has threshold t(n) = ( √ n). If t(n) = c √ n, then the limiting distribution for the number of vertices with multiple pebbles is Poisson(c). The threshold f...

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.