Suatu Hubungan Kumpulan Pusat–2 dengan Teori Kebarangkalian

2012 ◽  
Author(s):  
Nor Haniza Sarmin ◽  
Hasimah Sapiri
Keyword(s):  
Probability Theory ◽  
Finite Group ◽  
Finite Groups ◽  
Random Element ◽  
Symmetric Groups ◽  
Finite Rings ◽  
Nonabelian Group ◽  
Central Group ◽  
Upper Limit

Penentuan darjah keabelanan bagi suatu kumpulan tak abelan telah diperkenalkan untuk kumpulan simetri oleh Erdos dan Turan [1]. Dalam tahun 1973, Gustafson [2] mengkajinya bagi kumpulan terhingga sementara MacHale [3] mengkajinya bagi gelanggang terhingga dalam tahun 1976. Dalam kajian ini, beberapa keputusan yang berkaitan dengan Pn(G), kebarangkalian bahawa suatu unsur rawak dengan kuasa ke–n dalam suatu kumpulan pusat–2 G adalah kalis tukar tertib dengan unsur rawak yang lain dalam kumpulan yang sama, akan diberikan. Seterusnya, batas atas bagi P2(G) diperoleh. Kata kunci: Teori kebarangkalian, teori kumpulan, kumpulan terhingga, kalis tukar tertib The determination of the abelianness of a nonabelian group has been introduced for symmetric groups by Erdos & Turan [1]. In 1973, Gustafson [2] did this research for the finite groups while MacHale [3] determined the abelianness for finite rings in 1976. In this research, some results on Pn(G), the probability that the n–th power of a random element in a 2–central group G commutes with another random element from the same group, will be presented. Furthermore, the upper limit of P2(G) is obtained. Key words: Probability theory, group theory, finite group, commutative

More on the OD-Characterizability of a Finite Group

2011 ◽  
Vol 18 (04) ◽  
pp. 663-674 ◽  
Author(s):  
A. R. Moghaddamfar ◽  
S. Rahbariyan
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Symmetric Groups ◽  
Alternating Groups ◽  
Degree Pattern ◽  
Prime Graphs ◽  
A Finite Group ◽  
P 53 ◽  
Number Of Authors

The degree pattern of a finite group G was introduced in [10]. We say that G is k-fold OD-characterizable if there exist exactly k non-isomorphic finite groups with the same order and same degree pattern as G. When a group G is 1-fold OD-characterizable, we simply call it OD-characterizable. In recent years, a number of authors attempt to characterize finite groups by their order and degree pattern. In this article, we first show that for the primes p=53, 61, 67, 73, 79, 83, 89, 97, the alternating groups Ap+3 are OD-characterizable, while the symmetric groups Sp+3 are 3-fold OD-characterizable. Next, we show that the automorphism groups Aut (O7(3)) and Aut (S6(3)) are 6-fold OD-characterizable. It is worth mentioning that the prime graphs associated with all these groups are connected.

scholarly journals ON THE REGULARITY CONJECTURE FOR THE COHOMOLOGY OF FINITE GROUPS

2008 ◽  
Vol 51 (2) ◽  
pp. 273-284 ◽  
Author(s):  
David J. Benson
Keyword(s):  
Finite Group ◽  
Wreath Product ◽  
Finite Groups ◽  
Cohomology Ring ◽  
Symmetric Groups ◽  
Wreath Products ◽  
Characteristic P ◽  
Residue Classes ◽  
The Difference ◽  
A Finite Group

AbstractLet $K$ be a field of characteristic $p$ and let $G$ be a finite group of order divisible by $p$. The regularity conjecture states that the Castelnuovo–Mumford regularity of the cohomology ring $H^*(G,K)$ is always equal to 0. We prove that if the regularity conjecture holds for a finite group $H$, then it holds for the wreath product $H\wr\mathbb{Z}/p$. As a corollary, we prove the regularity conjecture for the symmetric groups $\varSigma_n$. The significance of this is that it is the first set of examples for which the regularity conjecture has been checked, where the difference between the Krull dimension and the depth of the cohomology ring is large. If this difference is at most 2, the regularity conjecture is already known to hold by previous work.For more general wreath products, we have not managed to prove the regularity conjecture. Instead we prove a weaker statement: namely, that the dimensions of the cohomology groups are polynomial on residue classes (PORC) in the sense of Higman.

Recognizing Finite Groups Through Order and Degree Pattern

2008 ◽  
Vol 15 (03) ◽  
pp. 449-456 ◽  
Author(s):  
A. R. Moghaddamfar ◽  
A. R. Zokayi
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Automorphism Groups ◽  
Symmetric Groups ◽  
Simple Groups ◽  
Alternating Groups ◽  
Degree Pattern ◽  
Sporadic Simple Groups ◽  
A Finite Group ◽  
Groups Of Lie Type

The degree pattern of a finite group G is introduced in [10] and it is proved that the following simple groups are uniquely determined by their degree patterns and orders: all sporadic simple groups, alternating groups Ap (p ≥ 5 is a twin prime) and some simple groups of Lie type. In this paper, we continue this investigation. In particular, we show that the automorphism groups of sporadic simple groups (except Aut (J2) and Aut (McL)), all simple C22-groups, the alternating groups Ap, Ap+1, Ap+2 and the symmetric groups Sp, Sp+1, where p is a prime, are also uniquely determined by their degree patterns and orders.

scholarly journals The embeddability of ring and semigroup amalgams is undecidable

2000 ◽  
Vol 69 (2) ◽  
pp. 272-286 ◽  
Author(s):  
Marcel Jackson
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Finite Rings ◽  
Marked Contrast ◽  
Finite Semigroups ◽  
A Finite Group

AbstractWe prove that there is no algorithm to determine when an amalgam of finite rings (or semigroups) can be embedded in the class of rings or in the class of finite rings (respectively, in the class of semigroups or in the class of finite semigroups). These results are in marked contrast with the corresponding problems for groups where every amalgam of finite groups can be embedded in a finite group.

scholarly journals Bounds on the Action Degree of Groups

MATEMATIKA ◽  
2019 ◽  
Vol 35 (2) ◽  
pp. 271-282
Author(s):  
S. Alrehaili ◽  
Charef Beddani
Keyword(s):  
Finite Group ◽  
Direct Product ◽  
Finite Groups ◽  
Random Element ◽  
General Relation ◽  
Finitely Generated ◽  
Finitely Generated Groups ◽  
A Finite Group

The commutativity degree is the probability that a pair of elements chosen randomly from a group commute. The concept of  commutativity degree has been widely discussed by several authors in many directions.  One of the important generalizations of commutativity degree is the probability that a random element from a finite group G fixes a random element from a non-empty set S that we call the action degree of groups. In this research, the concept of action degree is further studied where some inequalities and bounds on the action degree of finite groups are determined.  Moreover, a general relation between the action degree of a finite group G and a subgroup H is provided. Next, the action degree for the direct product of two finite groups is determined. Previously, the action degree was only defined for finite groups, the action degree for finitely generated groups will be defined in this research and some bounds on them are going to be determined.

Quantitative Radioisotope Measurement of Duodenogastric Reflux in Patients with Ulcer or Gastrectomized for Ulcer

1985 ◽  
Vol 24 (03) ◽  
pp. 107-110
Author(s):  
M. Pääkkönen ◽  
S. Aukee ◽  
K. Korhonen ◽  
A. Pääkkönen ◽  
E. Länsimies ◽  
...  
Keyword(s):  
Gamma Camera ◽  
Background Activity ◽  
Bile Reflux ◽  
Duodenogastric Reflux ◽  
Upper Limit ◽  
Visual Evidence ◽  
Biochemical Measurement

SummaryIn this work the duodenogastric reflux was quantified as the amount of radioactivity entering the stomach after an i.v. administration of 99mmTc-HIDA in ulcer patients and in patients who had undergone BI gastrectomy. The results were compared with visual evidence of gastric activity in the gamma camera images and biochemical determination of gastric bile reflux. The method is useful in quantifying the reflux if the activity is above the background activity. It allows the determination of an upper limit for the reflux when the reflux is evident visually. Only two or three images are needed for the quantitation. No correlation was found between biochemical measurement of fasting bile reflux in the stomach and radioisotopic quantification.

scholarly journals X-Ray Determination of the Black-Hole Mass in Cygnus X-1

1998 ◽  
Vol 188 ◽  
pp. 388-389
Author(s):  
A. Kubota ◽  
K. Makishima ◽  
T. Dotani ◽  
H. Inoue ◽  
K. Mitsuda ◽  
...  
Keyword(s):  
Black Hole ◽  
Compact Object ◽  
Optical Observations ◽  
Black Hole Mass ◽  
X Ray ◽  
Upper Limit ◽  
Supergiant Star ◽  
X Ray Binaries ◽  
Two Bodies

About 10 X-ray binaries in our Galaxy and LMC/SMC are considered to contain black hole candidates (BHCs). Among these objects, Cyg X-1 was identified as the first BHC, and it has led BHCs for more than 25 years(Oda 1977, Liang and Nolan 1984). It is a binary system composed of normal blue supergiant star and the X-ray emitting compact object. The orbital kinematics derived from optical observations indicates that the compact object is heavier than ~ 4.8 M⊙ (Herrero 1995), which well exceeds the upper limit mass for a neutron star(Kalogora 1996), where we assume the system consists of only two bodies. This has been the basis for BHC of Cyg X-1.

scholarly journals Finite groups with some weakly pronormal subgroups

2020 ◽  
Vol 18 (1) ◽  
pp. 1742-1747
Author(s):  
Jianjun Liu ◽  
Mengling Jiang ◽  
Guiyun Chen
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
A Finite Group

Abstract A subgroup H of a finite group G is called weakly pronormal in G if there exists a subgroup K of G such that G = H K G=HK and H ∩ K H\cap K is pronormal in G. In this paper, we investigate the structure of the finite groups in which some subgroups are weakly pronormal. Our results improve and generalize many known results.

scholarly journals Constraints on neutrino non-standard interactions from LHC data with large missing transverse momentum

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
DianYu Liu ◽  
ChuanLe Sun ◽  
Jun Gao
Keyword(s):  
Transverse Momentum ◽  
Neutral Current ◽  
Data Sets ◽  
Leading Order ◽  
Missing Transverse Momentum ◽  
Upper Limit ◽  
Theoretical Predictions ◽  
Parton Showering ◽  
Single Jet

Abstract The possible non-standard interactions (NSIs) of neutrinos with matter plays important role in the global determination of neutrino properties. In our study we select various data sets from LHC measurements at 13 TeV with integrated luminosities of 35 ∼ 139 fb−1, including production of a single jet, photon, W/Z boson, or charged lepton accompanied with large missing transverse momentum. We derive constraints on neutral-current NSIs with quarks imposed by different data sets in a framework of either effective operators or simplified Z′ models. We use theoretical predictions of productions induced by NSIs at next-to-leading order in QCD matched with parton showering which stabilize the theory predictions and result in more robust constraints. In a simplified Z′ model we obtain a 95% CLs upper limit on the conventional NSI strength ϵ of 0.042 and 0.0028 for a Z′ mass of 0.2 and 2 TeV respectively. We also discuss possible improvements from future runs of LHC with higher luminosities.

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