on nilpotent and solvable polygroups

On nilpotent and solvable polygroups

Applications of hypergroups have mainly appeared in special subclasses. One of the important subclasses is the class of polygroups. In this paper, we study the notions of nilpotent and solvable polygroups by using the notion of heart of polygroups. In particular, we give a necessary and sufficient condition between nilpotent (solvable) polygroups and fundamental groups.

Nilpotent and Solvable Numbers

Geometry of Nilpotent and Solvable Groups

(Answer 1) By defining a Cayley graph. Let S be a finite generating set for G , such that S−1 = {s−1 | s ∈ S} = S and 1 ̸∈ S . NB From now on we always assume that generating sets of the group that we consider satisfy the above. The Cayley graph Cayley(G,S) of G with respect to the generating set S is a non-oriented graph defined as follows: • its set of vertices is G ; • every pair of elements ...

Solvable and Nilpotent Sübalgebras of Lie Algebras

Solvable and Nilpotent Fuzzy Lie ∼ Ideal over Fuzzy Field

The commutator of Lie algebra is extended to a product of fuzzy Lie subspaces over fuzzy field. An action of fuzzy field is introduced as an extension of scalar multiplication in Lie algebra. The notion of derived series and descending central series of fuzzy Lie ∼ideal over fuzzy field and the concepts of ∼nilpotent and ∼solvable fuzzy Lie ∼ideals over fuzzy field are studied. Mathematics Subj...

Invariants of the nilpotent and solvable triangular Lie algebras

Invariants of the coadjoint representation of two classes of Lie algebras are calculated. The first class consists of the nilpotent Lie algebras T (M), isomorphic to the algebras of upper triangular M × M matrices. The Lie algebra T (M) is shown to have [M/2] functionally independent invariants. They can all be chosen to be polynomials and they are presented explicitly. The second class consist...