Characterization of finite simple group $ A_{p+3}$ by its order and degree pattern

2015 ◽  
Vol 86 (1-2) ◽  
pp. 19-30 ◽  
Author(s):  
ALI MAHMOUDIFAR ◽  
BEHROOZ KHOSRAVI
Keyword(s):  
Simple Group ◽  
Finite Simple Group ◽  
Degree Pattern

scholarly journals A characterization of the finite simple group 2D4(2)

1979 ◽  
Vol 60 (2) ◽  
pp. 552-558 ◽  
Author(s):  
Tran van Trung
Keyword(s):  
Simple Group ◽  
Finite Simple Group

On the Mathieu group M23

1971 ◽  
Vol 12 (4) ◽  
pp. 385-392 ◽  
Author(s):  
N. Bryce
Keyword(s):  
Simple Group ◽  
Finite Simple Group ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Unique Determination ◽  
Mathieu Group ◽  
Mathieu Groups

Until 1965, when Janko [7] established the existence of his finite simple group J1, the five Mathieu groups were the only known examples of isolated finite simple groups. In 1951, R. G. Stanton [10] showed that M12 and M24 were determined uniquely by their order. Recent characterizations of M22 and M23 by Janko [8], M22 by D. Held [6], and M11 by W. J. Wong [12], have facilitated the unique determination of the three remaining Mathieu groups by their orders. D. Parrott [9] has so characterized M22 and M11, while this paper is an outline of the characterization of M23 in terms of its order.

scholarly journals A characterization of the finite simple group M(23)

1973 ◽  
Vol 26 (3) ◽  
pp. 431-439 ◽  
Author(s):  
David C. Hunt
Keyword(s):  
Simple Group ◽  
Finite Simple Group

scholarly journals A Characterization of the finite simple group L4(3)

1969 ◽  
Vol 10 (1-2) ◽  
pp. 51-76 ◽  
Author(s):  
Kok-Wee Phan
Keyword(s):  
Simple Group ◽  
Finite Simple Group

In this paper we aim to give a characterization of the finite simple group L4(3) (i.e. PSL(4, 3)) by the structure of the centralizer of an involution contained in the centre of its Sylow 2-subgroup. More precisely, we shall prove the following result.

A characterization of the finite simple group L16(2) by its prime graph

2008 ◽  
Vol 126 (1) ◽  
pp. 49-58 ◽  
Author(s):  
Behrooz Khosravi ◽  
Bahman Khosravi ◽  
Behnam Khosravi
Keyword(s):  
Simple Group ◽  
Finite Simple Group ◽  
Prime Graph

Characterization of finite simple group D n (2)

2009 ◽  
Vol 5 (1) ◽  
pp. 179-190
Author(s):  
Lingli Wang
Keyword(s):  
Simple Group ◽  
Finite Simple Group ◽  
Group D

A Characterization of the Finite Simple Group PSp4(3)

1973 ◽  
Vol 25 (3) ◽  
pp. 539-553 ◽  
Author(s):  
John L. Hayden
Keyword(s):  
Simple Group ◽  
Finite Simple Group

The aim of this paper is to characterize the finite simple group PSp4(3) by the structure of the centralizer of an element of order three contained in the center of its Sylow 3-subgroup. More precisely, we shall prove the following results.

scholarly journals Zoology of Atlas-Groups: Dessins D’enfants, Finite Geometries and Quantum Commutation

2016 ◽  
Author(s):  
Michel Planat ◽  
Hishamuddin Zainuddin
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Finite Simple Group ◽  
Physical Significance ◽  
Simple Groups ◽  
Finite Geometries ◽  
Group Representations ◽  
Small Index ◽  
Point Line

Every finite simple group P can be generated by two of its elements. Pairs of generators forP are available in the Atlas of finite group representations as (not necessarily minimal) permutation representations P . It is unusual but significant to recognize that a P is a Grothendieck’s dessin d’enfant D and that a wealth of standard graphs and finite geometries G - such as near polygons and their generalizations - are stabilized by a D. In our paper, tripods P − D − G of rank larger than two,corresponding to simple groups, are organized into classes, e.g. symplectic, unitary, sporadic, etc (as in the Atlas). An exhaustive search and characterization of non-trivial point-line configurationsdefined from small index representations of simple groups is performed, with the goal to recognize their quantum physical significance. All the defined geometries G's have a contextuality parameterclose to its maximal value 1.

scholarly journals A Characterization of the Finite Simple Groups PSp(4, q), G2(q), I

1969 ◽  
Vol 36 ◽  
pp. 143-184 ◽  
Author(s):  
Paul Fong ◽  
W.J. Wong
Keyword(s):  
Simple Group ◽  
Finite Simple Group ◽  
Symplectic Group ◽  
Prime Power ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Central Product ◽  
Twisted Group ◽  
Index 2

Suppose that G is the projective symplectic group PSp(4, q), the Dickson group G2(q)> or the Steinberg “triality-twisted” group where q is an odd prime power. Then G is a finite simple group, and G contains an involution j such that the centralizer C(j) in G has a subgroup of index 2 which contains j and which is the central product of two groups isomorphic with SL(2,q1) and SL(2,q2) for suitable ql q2. We wish to show that conversely the only finite simple groups containing an involution with this property are the groups PSp(4,q), G2(q)9. In this first paper we shall prove the following result.

A Characterization of PSU11(q)

2004 ◽  
Vol 47 (4) ◽  
pp. 530-539 ◽  
Author(s):  
A. Iranmanesh ◽  
B. Khosravi
Keyword(s):  
Simple Group ◽  
Finite Simple Group ◽  
Simple Groups ◽  
Order Components

AbstractOrder components of a finite simple group were introduced in [4]. It was proved that some non-abelian simple groups are uniquely determined by their order components. As the main result of this paper, we show that groups PSU11(q) are also uniquely determined by their order components. As corollaries of this result, the validity of a conjecture of J. G. Thompson and a conjecture of W. Shi and J. Bi both on PSU11(q) are obtained.

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