In group theory nilpotency of a group has a great importance. In this paper we have studied some concept of nilpotency through right transversals. We have also studied prime power groups and frattini subgroups through right transversals.

We study the finite groups G for which the set cd(G) of irreducible complex character degrees consists of the two most extreme possible values, that is, 1 and |G : Z(G)|1/2. We are easily reduced to finite p-groups, for which we derive the following group theoretical characterization: they are the p-groups such that |G : Z(G)| is a square and whose only normal subgroups are those containing G′ ...

Metanilpotent Fitting classes are given consisting of groups with elementary abelian Fitting quotient and fairly wide choices of the nilpotency class of the nilpotent residual. Many of the minimal normal subgroups are non-central. AMS subject classiication 20D10 1 Key sections The aim of this note is to establish further examples of Fitting classes of metanilpotent groups to further the transpa...

In this paper we introduce the concept of α-commutator which its definition is based on generalized conjugate classes. With this notion, α-nilpotent groups, α-solvable groups, nilpotency and solvability of groups related to the automorphism are defined. N(G) and S(G) are the set of all nilpotency classes and the set of all solvability classes for the group G with respect to different automorphi...

We investigate the computational properties of cellular automata on countable (equivalently, zero entropy) sofic shifts with an emphasis on nilpotency, periodicity, and asymptotic behavior. As a tool for proving decidability results, we prove the Starfleet Lemma, which is of independent interest. We present computational results including the decidability of nilpotency and periodicity, the unde...

Let L be an algebra over a field F. Then is called left Leibniz if its multiplication operations [×, ×] addition- ally satisfy the so-called identity: [[a,b],c] = [a,[b,c]] – [b,[a,c]] for all elements a, b, c Î L. In this paper, we begin description of derivations algebras having dimension 3. It clear that algebras, 3, quite large. Therefore, in article, will focus on nilpotent algebra, whose ...