Related papers: Stabilizer group of generalized determinant
We study the problem of determining, for a polynomial function $f$ on a vector space $V$, the linear transformations $g$ of $V$ such that $f g = f$. In case $f$ is invariant under a simple algebraic group $G$ acting irreducibly on $V$, we…
This article deals with stability of continuous-time switched linear systems under constrained switching. Given a family of linear systems, possibly containing unstable dynamics, we characterize a new class of switching signals under which…
The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…
We explore some properties of a recent representation of permanental vectors which expresses them as sums of independent vectors with components that are independent gamma random variables.
We extend an operational characterization of entanglement in terms of stabilizer groups from pure states to mixed states. For a density matrix $\rho_{AB}$, a stabilizer is a factorized unitary matrix $u_A \otimes u_B$ that, under…
The problem of homological stability helps us to catch the structure of group homology. We calculate homological stability of special orthogonal groups, and we also calculate the stability of orthogonal groups with determinant-twisted…
A non-trivial element of a group is a generalized torsion element if some products of its conjugates is the identity. The minimum number of such conjugates is called a generalized torsion order. We provide several restrictions for…
We study $\mu$-stabilizers for groups definable in ACVF in the valued field sort. We prove that $\mathrm{Stab}^\mu(p)$ is an infinite unbounded definable subgroup of $G$ when $p$ is standard and unbounded. In the particular case when $G$ is…
This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…
In this paper, we consider some generalized commutator equations in a finite group and show that the number of solutions of such equations are characters of that group. We also obtain explicit formula for this character, considering the…
We study determinants of matrices whose entries are powers of Fibonacci numbers. We then extend the results to include entries that are powers of generalized Fibonacci numbers defined as a second-order linear recurrence relation. These…
We study special subgroups of infinite groups that generalize double centralizers. We analyze sufficient conditions for descending chains of such subgroups to stop after finitely many steps. We discuss whether this phenomenon can happen in…
This paper is devoted to the stabilization of a linear control system $y' = A y + B u$ and its suitable non-linear variants where $(A, \cD(A))$ is an infinitesimal generator of a strongly continuous {\it group} in a Hilbert space $\mH$, and…
We define a certain compactifiction of the general linear group and give a modular description for its points with values in arbitrary schemes. This is a first step in the construction of a higher rank generalization of Gieseker's…
For every group of order at most 14 we determine the values taken by its group determinant when its variables are integers.
In this paper we introduce the concept of generalized vector groupoid. Several properties of them are established.
A group G is called bounded if every conjugation-invariant norm on G has finite diameter. We introduce various strengthenings of this property and investigate them in several classes of groups including semisimple Lie groups, arithmetic…
This paper concerns a question that frequently occurs in various applications: Is any diffusive coupling of stable linear systems, also stable? Although it has been known for a long time that this is not the case, we shall identify a…
We study the stability of certain spectra under some algebraic conditions weaker than the commutativity and we generalize many known commutative perturbation results.
In this paper we propose a refinement of Sims conjecture concerning the cardinality of the point stabilizers in finite primitive groups and we make some progress towards this refinement. In this process, when dealing with primitive groups…