Number Of Centralizers Research Articles

On the conjecture of groups with the same number of centralizers

On the conjecture of groups with the same number of centralizers

On the number of centralizers and conjugacy class sizes in finite groups

Given a finite group G, denote by cs(G) the set of the sizes of the conjugacy classes of G and by Cent(G) the set of the centralizers of elements of G. Consider a prime p and integers s ≥ 2 and n ≥ 2 , with gcd ( p , s ) = 1 . In this paper, some relations between cs(G) and | Cent ( G ) | are established in the case where cs ( G ) = { 1 , p n , p n − 1 s } . Further, when p ∈ { 2 , 3 } , we determine the values of s and the structure of a finite group G such that cs ( G ) = { 1 , p n , p n − 1 s } . We also describe the structure of an AC-group G such that [ G : Z ( G ) ] = 3 n s and | Cent ( G ) | = 1 + ∑ i = 0 n 3 i , where gcd ( 3 , s ) = 1 .

On groups with same number of centralizers

ABSTRACT In this paper, among other results, we give some sufficient conditions for every non-abelian subgroup of a group to be isoclinic with the group itself. It is also seen that under certain conditions, two groups have same number of element centralizers implies they are isoclinic. We prove that if G is any group having 4, 5, 7 or 9 element centralizers and H is any non-abelian subgroup of G, then and or respectively. Furthermore, it is proved that if G is any group having element centralizers, then . Communicated by Mark Lewis

On finite rings with a certain number of centralizers

Let [Formula: see text] denote the set of all distinct centralizers in a ring [Formula: see text]. A ring [Formula: see text] is said to be [Formula: see text]-centralizer ring if [Formula: see text], where [Formula: see text]. In this paper, we illustrate some connections between the centralizers and pairwise non-commuting elements of a finite ring. Besides that, we characterize all [Formula: see text]-centralizer finite rings for [Formula: see text], and also compute the commuting probability for all [Formula: see text]-centralizer finite rings for [Formula: see text].

A note on the number of centralizers in finite AC-groups

Let [Formula: see text] be a finite AC-group such that [Formula: see text], where [Formula: see text], [Formula: see text] and [Formula: see text] is odd. We prove that if [Formula: see text] has [Formula: see text] centralizers of elements, then [Formula: see text], [Formula: see text] is an even integer, the set of the sizes of the conjugacy classes of [Formula: see text] is [Formula: see text] and [Formula: see text] is a Frobenius group whose Frobenius kernel is an elementary abelian [Formula: see text]-group of order [Formula: see text] and the Frobenius complement is a group of order [Formula: see text].

Groups with the same number of centralizers

For any group [Formula: see text], let [Formula: see text] denote the set of all non-abelian centralizers of [Formula: see text]. Jafarian Amiri and Rostami, Groups with a few nonabelian centralizers, Publ. Math. Debrecen 87(3–4) (2015) 429–437 put forward the following question: Let [Formula: see text] and [Formula: see text] be finite simple groups. Is it true that if [Formula: see text], then [Formula: see text] is isomorphic to [Formula: see text]? In this paper, among other things, we give a negative answer to this question.

Finite groups in which the centralizer of every noncentral element of odd order is abelian

In this paper, we consider the influence of the number of centralizers of noncentral elements of odd order on the solvability of finite groups. Also, we characterize some finite groups in which the centralizer of every noncentral element of odd order is abelian.

Lateral Buckling Theory and Experimental Study on Pipe-in-Pipe Structure

With the increasing depth of marine oil and gas exploitation, more requirements have been proposed on the structure of deep-sea oil pipelines. The influencing factors of lateral buckling of a pipe-in-pipe (PIP) structure containing initial imperfections and its critical force were investigated in this study by conducting an experiment, a finite element analysis, and a theoretical derivation. The change laws on the influence of initial imperfections of the PIP structure during thermal loading were revealed through an experimental study by using imperfection amplitude and wavelength as parameters. Appropriate finite element models were established, and the influences of initial imperfections, pipe-soil interaction, and the height and the number of centralizers on the global buckling critical force of the PIP structure were analyzed. The formulas of global buckling critical force of inner and outer pipes and that under pipe-soil interaction was obtained by using a theoretical derivation method. A comparative verification with experimental and finite element (FE) models result was conducted, which provided a corresponding basis for steel pipeline design.

Centralizers in a group whose central factor is simple

In this paper, we find the number of the element centralizers of a finite group [Formula: see text] such that the central factor of [Formula: see text] is the projective special linear group of degree 2 or the Suzuki group. Our results generalize some main results of [Ashrafi and Taeri, On finite groups with a certain number of centralizers, J. Appl. Math. Comput. 17 (2005) 217–227; Schmidt, Zentralisatorverbände endlicher Gruppen, Rend. Sem. Mat. Univ. Padova 44 (1970) 97–131; Zarrin, On element centralizers in finite groups, Arch. Math. 93 (2009) 497–503]. Also, we give an application of these results.

Continuous Innovation Achieves Better Zonal Isolation in Extended-Reach Wells

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 188295, “Success Through Continuous Innovation To Achieve Better Zonal Isolation in Extended-Reach Wells in a UAE Field,” by Abdelkerim Doutoum Mahamat Habib, SPE, Yousif Saleh Al Katheeri, Sheldon Seales, SPE, Rayaz Evans Ramdeen, Romulo Francisco Bermudez, SPE, and Luis Eduardo Navas, SPE, ZADCO; and Saurabh Kapoor, SPE, Surya Pallapothu, Azza El Hassan, and Bipin Jain, SPE, Schlumberger, prepared for the 2017 Abu Dhabi International Petroleum Exhibition and Conference, Abu Dhabi, 13–16 November. The paper has not been peer reviewed. Operators at a UAE field experienced several challenges while cementing production sections. A systematic approach was applied that used standard cementing best practices as a starting point. An advanced cement-placement software was used to model prejob circulation rates, bottomhole circulating temperatures, centralizer placement, and mud removal. To enhance conventional chemistry-based mud cleaning, an engineered fiber-based scrubbing additive was used in spacers with a microemulsion-based surfactant. Finally, real-time monitoring software was used to evaluate cement placement in real time. Introduction Artificial islands are built in the UAE to reduce life-cycle development costs and enable long-term maximum recovery levels by accommodating up to 300 wellheads on a single island. The wells drilled from these islands are complex extended-reach horizontal laterals with measured depths planned at more than 35,000 ft. Cementing these wells is extremely challenging, largely because of long open holes with high deviation, the use of nonaqueous fluids (NAFs) for shale stability, and lost circulation while drilling and cementing. Additional stringent prerequisites, such as casing pressure tests at high pressures after the cement is set and the need to isolate narrowly separated sublayers of reservoir, increase the complexity of cementing these wells. This paper demonstrates the continuous improvements in the prevailing stepwise approach and the role of the improvements in attaining needed zonal isolation. These improvements can be divided into four main sections: Advanced cement-placement modeling Engineered fiber-based scrubbing agents in spacers Engineered flexible expanding cement systems Real-time cement-job monitoring Advanced Cement-Placement Modeling Good casing centralization during cementing operations is key to achieving proper mud displacement and obtaining hydraulic isolation in the annulus. To this end, centralizers are often placed along the casing to position it centrally in the borehole. The optimal number of centralizers and their spacing are determined through software simulations. Until now, the industry typically has used calculation methods derived from American Petroleum Institute Specification 10D to predict casing eccentricity in the wellbore. The calculations are based on an analytical soft-string method, which models an element of casing string between two centralizers as a bifixed beam. However, for extended-reach wells, the use of a numerical stiff-string method to compute torque-and-drag forces is becoming increasingly popular. It accounts for tubular bending stiffness and provides a more-realistic analysis of the stresses and loads acting on the drill-string and the borehole. The stiff-string technique, based on the finite-element method, is, therefore, proposed as an alternative and more-effective solution for computing casing centralization for cementing operations, especially in deviated sections.

Centralizers in Lie Algebras

We determine the number of centralizers of different non-abelian finite dimensional Lie algebras over a specific field. Also, the concept of Lie algebras with abelian centralizers are studied and using a result of Bokut and Kukin [5], for a given residually free Lie algebra L, it is shown that L is fully residually free if and only if every centralizer of non-zero elements of L is abelian.

On the maximum number of the pairwise noncommuting elements in a finite group

For a finite group [Formula: see text], let [Formula: see text] be the maximum size of a set of pairwise noncommuting elements in [Formula: see text]. In this paper, we give an upper bound of [Formula: see text] for an arbitrary nilpotent group [Formula: see text]. As an application of this result, we give a partial answer to Question 2.8 of [A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloq. 7(2) (2000) 139–146]. Also we compute [Formula: see text] when [Formula: see text] is a Frobenius group. Finally we describe structural properties of all groups [Formula: see text] with [Formula: see text].

Finite groups determined by the number of element centralizers

ABSTRACTFor a finite group G, let |Cent(G)| and ω(G) denote the number of centralizers of its elements and the maximum size of a set of pairwise noncommuting elements of it, respectively. A group G is called n-centralizer if |Cent(G)| = n and primitive n-centralizer if . In this paper, among other results, we find |Cent(G)| and ω(G) when is minimal nonabelian and this generalizes some previous results. We give a necessary and sufficient condition for a primitive n-centralizer group G with the minimal nonabelian central factor. Also we show that if , then G is a primitive 14-centralizer group and ω(G) = 10 or 13. Finally we confirm Conjecture 2.4 in [A. R. Ashrafi, On finite groups with a given number of centralizers, Algebra Colloq. 7(2) (2000), 139-146].

A Note on the Number of Centralizers in Finite Groups

A Note on the Number of Centralizers in Finite Groups

Surge and Drag Analysis for Extended Reach Casing and Casing Flotation Operations With Centralizers: A Design Challenge?

Summary Refining advanced technologies for the successful completion of wells is paramount in high-risk, high-cost environments. Challenges are associated with complex well architectures and with the successful completion of wells deploying conventional or floated casing or liner strings. A key part of the design process is to be able to predict both maximum downhole surge pressures and dynamic and static friction effects. The analysis also needs to take into account the impact of using centralizing devices. Understanding these effects during both casing running and reciprocation is important so that appropriate operational decisions can be made. Specific challenges are associated with running liners through casing strings or hole sections with limited annular clearance. Centralizers are primarily installed on a casing string to provide adequate stand-off for primary cementing operations; however they are also sometimes used to aid in the deployment of casing strings. To achieve adequate stand-off, calculations are performed to determine the number of centralizers, their placement, and spacing frequency. Drag modeling is performed to ensure that the casing string will reach its target depth. This requires predictions of both static and dynamic drag effects that take into account the impact of centralizers and surge pressures on drag. In cases where non-rigid centralizers are used, conventional torque and drag models underestimate frictional drag effects. Similarly it is considered that steady state surge models under-predict maximum surge pressures. To address these concerns, both improved models and comprehensive analysis are required. This paper describes the analytical models that are used to incorporate additional forces associated with centralizers. Both conventional and floated casing running scenarios, especially in close tolerance extended reach wells, are considered.

On Finite Groups with a Given Number of Centralizers

For a finite group G, let Cent(G) denote the set of centralizers of single elements of G and #Cent(G) = |Cent(G)|. G is called an n-centralizer group if #Cent(G) = n, and a primitive n-centralizer group if #Cent(G) = #Cent(G/Z(G)) = n. In this paper, we compute #Cent(G) for some finite groups G and prove that, for any positive integer n ≠ 2, 3, there exists a finite group G with #Cent(G) = n, which is a question raised by Belcastro and Sherman [2]. We investigate the structure of finite groups G with #Cent(G) = 6 and prove that, if G is a primitive 6-centralizer group, then G/Z(G) ≅ A4, the alternating group on four letters. Also, we prove that, if G/Z(G) ≅ A4, then #Cent(G) = 6 or 8, and construct a group G with G/Z(G) ≅ A4 and #Cent(G) = 8.

On Finite Groups with a Given Number of Centralizers

For a finite group G, let Cent(G) denote the set of centralizers of single elements of G and #Cent(G) = |Cent(G)|. G is called an n-centralizer group if #Cent(G) = n, and a primitive n-centralizer group if #Cent(G) = #Cent(G/Z(G)) = n. In this paper, we compute #Cent(G) for some finite groups G and prove that, for any positive integer n ≠ 2, 3, there exists a finite group G with #Cent(G) = n, which is a question raised by Belcastro and Sherman [2]. We investigate the structure of finite groups G with #Cent(G) = 6 and prove that, if G is a primitive 6-centralizer group, then G/Z(G) ≅ A4, the alternating group on four letters. Also, we prove that, if G/Z(G) ≅ A4, then #Cent(G) = 6 or 8, and construct a group G with G/Z(G) ≅ A4 and #Cent(G) = 8.