We study the combinatorics of constructing non-singular geometrically irreducible projective curves that do not admit rational points over finite solvable extensions of the base field. A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c...

A Lie algebra is said to be metric if it admits a symmetric, invariant, and non-degenerate bilinear form. The harmonic oscillator algebra, which arises in the quantum mechanical description of oscillator, smallest solvable non-abelian example. This first step countable series algebras that support invariant Lorentzian forms. Generalizing this situation, paper, we arrive at K-algebras as double ...

A difficult problem in the character theory of solvable groups is to show that the number c.d. (G) of irreducible character degrees of a solvable group G is equal to or greater than d.l. (G), the derived length of G. Isaacs [4] has shown that d.l. (G) ^ 3 c.d. (G)-2 for every solvable group. Berger [1] subsequently proved that d.l. (G) < c.d. (G) when | G | is odd. This problem belongs to the c...

We give new information about the relationship between the lowdimensional homology of a group and its derived series. This yields information about how the low-dimensional homology of a topological space constrains its fundamental group. Applications are given to detecting when a set of elements of a group generates a subgroup “large enough” to map onto a non-abelian free solvable group, and to...

‎let $g$ be a finite group and let $n$ be a normal subgroup of $g$‎. ‎suppose that ${rm{irr}} (g | n)$ is the set of the irreducible characters of $g$ that contain $n$ in their kernels‎. ‎in this paper‎, ‎we classify solvable groups $g$ in which the set $mathcal{c} (g) = {{rm{irr}} (g | n) | 1 ne n trianglelefteq g }$ has at most three elements‎. ‎we also compute the set $mathcal{c}(g)$ for suc...

Received (received date) Revised (revised date) An algorithm and a computer program in Fortran 95 are presented which enumerate the Hugenholtz diagram representation of the many-body perturbation series for the ground state energy with a two-body interaction. The output is in a form suitable for post-processing such as automatic code generation. The results of a particular application, generati...

We investigate subgroups of the group PLo(I) of piecewise-linear, orientation preserving homeomorphisms of the unit interval with finitely many breaks in slope, and also subgroups of Thompson’s group F . We find geometric criteria determining the derived length of any such group, and use this criteria to classify the solvable and non-solvable subgroups of PLo(I) and of F . Let H be a subgroup o...

Using the formalism of supersymmetric quantum mechanics, we obtain a large number of new analytically solvable one-dimensional periodic potentials and study their properties. More specifically, the supersymmetric partners of the Lamé potentials ma(a+ 1) sn(x,m) are computed for integer values a = 1, 2, 3, .... For all cases (except a = 1), we show that the partner potential is distinctly differ...

Abstract. A case of the matrix Kummer relation of Herz (1955) based on the Pearson VII type matrix model is derived in this paper. As a con- sequence, the polynomial Pearson VII configuration density is obtained and this sets the corresponding exact inference as a solvable aspect in shape theory. An application in postcode recognition, including a nu- merical comparison between the exact poly...

In the literature two notions of the word problem for a variety occur. A variety has a decidable word problem if every finitely presented algebra in the variety has a decidable word problem. It has a uniformly decidable word problem if there is an algorithm which given a finite presentation produces an algorithm for solving the word problem of the algebra so presented. A variety is given with f...