Simple Linear Group Research Articles

Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups

Nonpronormal Subgroups of Odd Index in Finite Simple Linear and Unitary Groups

Special Unipotent Representations of Simple Linear Lie Groups of Type A

Special Unipotent Representations of Simple Linear Lie Groups of Type A

INVESTIGATION OF THE EFFECT OF SOCIAL MEDIA MARKETING ON DOCTOR BRANDING IN THE HEALTH SECTOR

In this research, it was conducted to examine the effect of social media marketing on doctor branding. In line with the purpose of the research; 547 people selected by simple random sampling method among the students continuing their education at the university constitute the research sample group and the data were collected by applying a face-to-face questionnaire. In the research, "Personal Information Form", "Social Media Marketing Scale in the Health Sector" and "Doctor Branding Scale" were used. Data were analyzed with SPSS. As a result of determining that the data are normally distributed as a method of analysis; simple linear regression, pearson correlation, ANOVA and independent groups t test were applied. As a result of the research, it was determined that the social media marketing of the participants had a statistically significant and positive effect on doctor branding. In the light of these results, it is predicted that the level of doctor branding will increase as individuals increase social media marketing in the health sector.

On recognition of direct powers of finite simple linear groups by spectrum

On recognition of direct powers of finite simple linear groups by spectrum

Topological and Homological Properties of the Orbit Space of a Simple Three-Dimensional Compact Linear Lie Group

Topological and Homological Properties of the Orbit Space of a Simple Three-Dimensional Compact Linear Lie Group

On the Helgason-Johnson bound

Let $G$ be a simple non-compact linear Lie group. Let $\pi$ be any irreducible unitary representation of $G$ with infinitesimal character $\Lambda$ whose continuous part is $\nu$. The beautiful Helgason-Jonson bound in 1969 says that the norm of $\nu$ is upper bounded by the norm of $\rho(G)$, which stands for the half sum of the positive roots of $G$. The current paper aims to give a framework to sharpen the Helgason-Johnson bound when $\pi$ is infinite-dimensional. We have explicit results for exceptional Lie groups. Ingredients of the proof include Parathasarathy's Dirac operator inequality, Vogan pencil, and the unitarily small convex hull introduced by Salamanca-Riba and Vogan.

Random walks on hyperbolic spaces: Concentration inequalities and probabilistic Tits alternative

The goal of this article is two-fold: in a first part, we prove Azuma–Hoeffding type concentration inequalities around the drift for the displacement of non-elementary random walks on hyperbolic spaces. For a proper hyperbolic space M, we obtain explicit bounds that depend only on M, the size of support of the measure as in the classical case of sums of independent random variables, and on the norm of the driving probability measure in the left regular representation of the group of isometries. We obtain uniform bounds in the case of hyperbolic groups and effective bounds for simple linear groups of rank-one. In a second part, using our concentration inequalities, we give quantitative finite-time estimates on the probability that two independent random walks on the isometry group of a hyperbolic space generate a free non-abelian subgroup. Our concentration results follow from a more general, but less explicit statement that we prove for cocycles which satisfy a certain cohomological equation. For example, this also allows us to obtain subgaussian concentration bounds around the top Lyapunov exponent of random matrix products in arbitrary dimension.

Topological and homological properties of the orbit space of a simple three-dimensional compact linear Lie group

Topological and homological properties of the orbit space of a simple three-dimensional compact linear Lie group

Normalizers of Sylow subgroups in finite linear and unitary groups

We specify normalizers of Sylow r-subgroups in finite simple linear and unitary groups for the case where r is an odd prime distinct from the characteristic of a definition field of a group.

Normalizers of Sylow Subgroups in Finite Linear and Unitary Groups

We specify normalizers of Sylow r-subgroups in finite simple linear and unitary groups for the case where r is an odd prime distinct from the characteristic of a definition field of a group.

On Finite Simple Linear and Unitary Groups of Small Size over Fields of Different Characteristics with Coinciding Prime Graphs

On Finite Simple Linear and Unitary Groups of Small Size over Fields of Different Characteristics with Coinciding Prime Graphs

Dirac index and associated cycles of Harish-Chandra modules

Let GR be a simple real linear Lie group with maximal compact subgroup KR and assume that rank(GR)=rank(KR). For any representation X of Gelfand-Kirillov dimension 12dim⁡(GR/KR), we consider the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing X. Under a technical condition involving the Springer correspondence, we establish an explicit relationship between this polynomial and the multiplicities of the irreducible components occurring in the associated cycle of X. This relationship was conjectured in [12].

On Finite Simple Linear and Unitary Groups over Fields of Different Characteristics with Coinciding Prime Graphs. I

Suppose that G is a finite group, π(G) is the set of prime divisors of its order, and ω(G) is the set of orders of its elements. We define a graph on π(G) with the following adjacency relation: different vertices r and s from π(G) are adjacent if and only if rs ∈ ω(G). This graph is called the Gruenberg-Kegel graph or the prime graph of G and is denoted by GK(G). In a series of papers, we describe the coincidence conditions for the prime graphs of nonisomorphic simple groups. This issue is connected with Vasil’ev’s Question 16.26 in the Kourovka Notebook about the number of nonisomorphic simple groups with the same prime graph. Earlier the author derived necessary and sufficient conditions for the coincidence of the prime graphs of two nonisomorphic finite simple groups of Lie type over fields of orders q and q1, respectively, with the same characteristic. Let G and G1 be two nonisomorphic finite simple groups of Lie type over fields of orders q and q1, respectively, with different characteristics. The author also obtained necessary conditions for the coincidence of the prime graphs of two nonisomorphic finite simple groups of Lie type. In the present paper the latter result is refined in the case where G is a simple linear group of sufficiently high Lie rank over a field of order q. If G is a simple linear group of sufficiently high Lie rank, then we prove that the prime graphs of G and G1 may coincide only in one of the nineteen cases. As corollaries of the main result, we obtain constraints (under some additional conditions) on the possible number of simple groups whose prime graph is the same as the prime graph of a simple linear group.

Computing the associated cycles of certain Harish-Chandra modules

Let Gℝ be a simple real linear Lie group with maximal compact subgroup Kℝ and assume that rank(Gℝ)=rank(Kℝ). In [17] we proved that for any representation X of Gelfand-Kirillov dimension 1/2dim(Gℝ/Kℝ), the polynomial on the dual of a compact Cartan subalgebra given by the dimension of the Dirac index of members of the coherent family containing X is a linear combination, with integer coefficients, of the multiplicities of the irreducible components occurring in the associated cycle. In this paper we compute these coefficients explicitly.

Periodic Groups Saturated with the Linear Groups of Degree 2 and the Unitary Groups of Degree 3 over Finite Fields of Odd Characteristic

Let M denote the set of the simple 3-dimensional unitary groups U3 and the simple linear groups L2 over finite fields of odd characteristic.We prove that each periodic group saturated with groups in M is locally finite and isomorphic to either U3(Q) or L2(Q) for a suitable locally finite field Q of odd characteristic.

The solvable subgroups of large order of L2(p) , p≥5

By using the following theoretical and computational algorithms , we determined the solvable subgroups of large order of the finite non-abelian simple linear groups G = L2(p) = PSL(2,p) , for p≥5 and p is a prime number , also their presentations and permutation representations have been found .

DOMAINS OF HOLOMORPHY FOR IRREDUCIBLE ADMISSIBLE UNIFORMLY BOUNDED BANACH REPRESENTATIONS OF SIMPLE LIE GROUPS

In this note, we address a question raised by B. Krotz on the classification of G-invariant domains of holomorphy for irreducible admissible Banach representations of connected non-compact simple real linear Lie groups G. When G is not of Hermitian type, we give a complete description of such G-invariant domains for irreducible admissible uniformly bounded representations on reflexive Banach spaces and, in particular, for all irreducible uniformly bounded Hilbert representations. When the group G is Hermitian, we determine such G-invariant domains only when the representations considered are highest or lowest weight representations.

Characterizations of Simple Linear Groups in the Class of Periodic Groups

Characterizations of Simple Linear Groups in the Class of Periodic Groups

On the uniform spread of almost simple symplectic and orthogonal groups

A group is 32-generated if every non-identity element is contained in a generating pair. A conjecture of Breuer, Guralnick and Kantor from 2008 asserts that a finite group is 32-generated if and only if every proper quotient of the group is cyclic, and recent work of Guralnick reduces this conjecture to almost simple groups. In this paper, we prove a stronger form of the conjecture for almost simple symplectic and odd-dimensional orthogonal groups. More generally, we study the uniform spread of these groups, obtaining lower bounds and related asymptotics. This builds on earlier work of Burness and Guest, who established the conjecture for almost simple linear groups.

On orders of elements of finite almost simple groups with linear or unitary socle

Abstract We say that a finite almost simple G with socle S is admissible (with respect to the spectrum) if G and S have the same sets of orders of elements. Let L be a finite simple linear or unitary group of dimension at least three over a field of odd characteristic. We describe admissible almost simple groups with socle L. Also we calculate the orders of elements of the coset L ⁢ τ {L\tau} , where τ is the inverse-transpose automorphism of L.