Solvable and nilpotent right loops

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

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.

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