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...

A wide range of dynamical systems from elds as diverse as mechanics, electrical networks and molecular chemistry can be modeled by invariant systems on matrix Lie groups. This paper extends the concept of approximate tracking in the high-frequency limit to non-nilpotent three-dimensional matrix Lie groups by making use of feedback nilpotentization for the local representations of these systems....

A problem of reducing intuitionistic fuzzy matrices is examined and some useful properties are obtained with respect to nilpotent intutionistic fuzzy matrices. First, reduction of irreflexive and transitive intuitionistic fuzzy matrices are considered, and then the properties are applied to nilpotent intutionistic fuzzy matrices. Nilpotent intuitionistic fuzzy matrices are intuitionistic fuzzy ...

In this article, we introduce two new generalized inverses for rectangular matrices called $W$-weighted generalized-Drazin--Moore--Penrose (GDMP) and generalized-Drazin-reflexive (GDR) inverses. The first inverse can be seen as a generalization of the recently introduced GDMP square matrix to matrix. second class contains inverse. We then exploit their various properties establish that proposed...

This paper explains a method of constructing algebras, starting with the properties discrimination in elementary discrete systems. We show how to use points view about these systems construct what we call iterant algebras and naturally give rise complex numbers, Clifford matrix algebras. The discusses structure Schrödinger equation, Dirac equation Majorana equations, finding solutions via nilpo...

Let Mn be the vector space of all n × n-matrices over an algebraically closed field F of characteristic zero. We describe the linear span of the conjugacy class (with respect to the full linear group GLn) of an arbitrary matrix A ∈ Mn, and derive the existence of some particular bases of Mn. Moreover, we propose certain observations on finite sequences of nilpotent matrices and their linear spa...

We find a minimal generating set for the defining ideal of the schematic intersection of the set of diagonal matrices with the closure of the conjugacy class of a nilpotent matrix indexed by a hook partition. The structure of this ideal allows us to compute its minimal free resolution and give an explicit description of the graded Betti numbers, and study its Hilbert series and regularity.

In this work we state a simple criterion for nilpotentness of a square n×n matrix pencil with respect to the action of SLn(C)×SLn(C)×SL2(C). The orbits of matrix pencils are classified explicitly for n = 4 and the hierarchy of closures of nilpotent orbits is described. Also, we prove that the algebra of invariants of the action of SLn(C)× SLn(C)× SL2(C) on C ⊗ C ⊗ C is isomorphic to the algebra...

We reduce the graph isomorphism problem to 2-nilpotent p-groups isomorphism problem (and to finite 2-nilpotent Lie algebras the ring Z/pZ. Furthermore, we show that classifying problems in categories graphs, finite 2-nilpotent p-groups, and 2-nilpotent Lie algebras over Z/pZ are polynomially equivalent and wild.

In the first part, we prove that the dominion (in the sense of Isbell) of a subgroup of a finitely generated nilpotent group is trivial in the category of all nilpotent groups. In the second part, we show that the dominion of a subgroup of a finitely generated nilpotent group of class two is trivial in the category of all metabelian nilpotent groups. Section