We exhibit counterexamples to a Conjecture of Nesin, since we build a connected solvable group with finite center and of finite Morley rank in which no normal nilpotent subgroup has a nilpotent complement. The main result says that each centerless connected solvable group G of finite Morley has a normal nilpotent subgroup U and an abelian subgroup T such that G = U o T , if and only if, for any...

If R is a binomial ring, then a nilpotent R-powered group G is termed power-commutative if for any α ∈ R, [gα, h] = 1 implies [g, h] = 1 whenever gα 6= 1. In this paper, we further contribute to the theory of nilpotent R-powered groups. In particular, we prove that if G is a nilpotent R-powered group of finite type which is not of finite π-type for any prime π ∈ R, then G is PC if and only if i...

We prove that any Novikov algebra over a field of characteristic [Formula: see text] is Lie-solvable if and only its commutator ideal right nilpotent. also construct examples infinite-dimensional algebras with non-nilpotent text].

The derivation of the exact and unique nilpotent Becchi-Rouet-Stora-Tyutin (BRST)and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of superfield approach to BRST formalism. These nilpotent symmetry transformations are deduced for the four (3 + 1)-dimensional (4D) complex scalar fields, coupled to ...

This is the first of a series of papers devoted to certain pairs of commuting nilpotent elements in a semisimple Lie algebra that enjoy quite remarkable properties and which are expected to play a major role in Representation theory. The properties of these pairs and their role is similar to those of the principal nilpotents. To any principal nilpotent pair we associate a two-parameter analogue...

We show that the dimension of the minimal nilpotent coadjoint orbit for a complex simple Lie algebra is equal to twice the dual Coxeter number minus two. Let g be a finite dimensional complex simple Lie algebra. We fix a Cartan subalgebra h, a root system ∆ ⊂ h and a set of positive roots ∆+ ⊂ ∆. Let ρ be half the sum of all positive roots. Denote by θ the highest root and normalize the Killing...