scholarly journals Families of solvable Frobenius subgroups in finite groups

2002 ◽  
Vol 165 ◽  
pp. 117-121
Author(s):  
Paul Lescot
Keyword(s):  
Finite Group ◽  
Linear Group ◽  
Finite Groups ◽  
Special Linear Group ◽  
Famous Result ◽  
Rank 2 ◽  
Characteristic 2 ◽  
A Finite Group ◽  
Suzuki Groups ◽  
Degenerate Cases

We introduce the notion of abelian system on a finite group G, as a particular case of the recently defined notion of kernel system (see this Journal, September 2001). Using a famous result of Suzuki on CN-groups, we determine all finite groups with abelian systems. Except for some degenerate cases, they turn out to be special linear group of rank 2 over fields of characteristic 2 or Suzuki groups. Our ideas were heavily influenced by [1] and [8].

Centralizers in a group whose central factor is simple

2018 ◽  
Vol 17 (08) ◽  
pp. 1850149
Author(s):  
Seyyed Majid Jafarian Amiri ◽  
Hojjat Rostami
Keyword(s):  
Finite Group ◽  
Linear Group ◽  
Finite Groups ◽  
Special Linear Group ◽  
Projective Special Linear Group ◽  
Special Linear ◽  
Central Factor ◽  
Suzuki Group ◽  
A Finite Group ◽  
Appl Math

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.

scholarly journals Finite automorphism groups of laminated near-rings

1983 ◽  
Vol 26 (3) ◽  
pp. 297-306 ◽  
Author(s):  
K. D. Magill ◽  
P. R. Misra ◽  
U. B. Tewari
Keyword(s):  
Finite Group ◽  
Linear Group ◽  
Complex Plane ◽  
Finite Groups ◽  
Automorphism Groups ◽  
The Other ◽  
Complex Polynomial ◽  
Infinite Groups ◽  
Nonsingular Matrices ◽  
A Finite Group

In [3] we initiated our study of the automorphism groups of a certain class of near-rings. Specifically, let P be any complex polynomial and let P denote the near-ring of all continuous selfmaps of the complex plane where addition of functions is pointwise and the product fg of two functions f and g in P is defined by fg=f∘P∘g. The near-ring P is referred to as a laminated near-ring with laminating element P. In [3], we characterised those polynomials P(z)=anzn + an−1zn−1 +…+a0 for which Aut P is a finite group. We are able to show that Aut P is finite if and only if Deg P≧3 and ai ≠ 0 for some i ≠ 0, n. In addition, we were able to completely determine those infinite groups which occur as automorphism groups of the near-rings P. There are exactly three of them. One is GL(2) the full linear group of all real 2×2 nonsingular matrices and the other two are subgroups of GL(2). In this paper, we begin our study of the finite automorphism groups of the near-rings P. We get a result which, in contrast to the situation for the infinite automorphism groups, shows that infinitely many finite groups occur as automorphism groups of the near-rings under consideration. In addition to this and other results, we completely determine Aut P when the coefficients of P are real and Deg P = 3 or 4.

scholarly journals Structure of intersection graphs

2021 ◽  
Vol 5 (2) ◽  
pp. 102
Author(s):  
Haval M. Mohammed Salih ◽  
Sanaa M. S. Omer
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Special Linear Group ◽  
Intersection Graph ◽  
Graph Structure ◽  
Normal Subgroups ◽  
Intersection Graphs ◽  
Cyclic Groups ◽  
A Finite Group

<p style="text-align: left;" dir="ltr"> Let <em>G</em> be a finite group and let <em>N</em> be a fixed normal subgroup of <em>G</em>.  In this paper, a new kind of graph on <em>G</em>, namely the intersection graph is defined and studied. We use <img src="/public/site/images/ikhsan/equation.png" alt="" width="6" height="4" /> to denote this graph, with its vertices are all normal subgroups of <em>G</em> and two distinct vertices are adjacent if their intersection in <em>N</em>. We show some properties of this graph. For instance, the intersection graph is a simple connected with diameter at most two. Furthermore we give the graph structure of <img src="/public/site/images/ikhsan/equation_(1).png" alt="" width="6" height="4" /> for some finite groups such as the symmetric, dihedral, special linear group, quaternion and cyclic groups. </p>

scholarly journals On recognition by prime graph of the projective special linear group over GF(3)

2014 ◽  
Vol 95 (109) ◽  
pp. 255-266
Author(s):  
Bahman Khosravi ◽  
Behnam Khosravi ◽  
Oskouei Dalili
Keyword(s):  
Finite Group ◽  
Simple Group ◽  
Linear Group ◽  
Prime Graph ◽  
Special Linear Group ◽  
Composition Factor ◽  
Projective Special Linear Group ◽  
Special Linear ◽  
A Finite Group ◽  
Nonabelian Composition Factor

Let G be a finite group. The prime graph of G is denoted by ?(G). We prove that the simple group PSLn(3), where n ? 9, is quasirecognizable by prime graph; i.e., if G is a finite group such that ?(G) = ?(PSLn(3)), then G has a unique nonabelian composition factor isomorphic to PSLn(3). Darafsheh proved in 2010 that if p > 3 is a prime number, then the projective special linear group PSLp(3) is at most 2-recognizable by spectrum. As a consequence of our result we prove that if n ? 9, then PSLn(3) is at most 2-recognizable by spectrum.

scholarly journals Finite groups of conjugate rank 2

1974 ◽  
Vol 53 ◽  
pp. 47-57 ◽  
Author(s):  
Alan R. Camina
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Conjugacy Classes ◽  
Rank 2 ◽  
A Finite Group

In 1953 N. Itô defined the conjugate rank of a finite group as the number of distinct sizes, not equal to 1, of the conjugacy classes of the group [7].

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 A on simplicity criterion for finite groups

1969 ◽  
Vol 10 (3-4) ◽  
pp. 359-362
Author(s):  
Nita Bryce
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Finite Groups ◽  
Odd Order ◽  
A Finite Group

M. Suzuki [3] has proved the following theorem. Let G be a finite group which has an involution t such that C = CG(t) ≅ SL(2, q) and q odd. Then G has an abelian odd order normal subgroup A such that G = CA and C ∩ A = 〈1〉.

On S-Quasinormal and C-Normal Subgroups of Prime Power Order in Finite Groups

2011 ◽  
Vol 18 (04) ◽  
pp. 685-692
Author(s):  
Xuanli He ◽  
Shirong Li ◽  
Xiaochun Liu
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Prime Power ◽  
Maximal Subgroups ◽  
Prime Power Order ◽  
Normal Subgroups ◽  
A Finite Group

Let G be a finite group, p the smallest prime dividing the order of G, and P a Sylow p-subgroup of G with the smallest generator number d. Consider a set [Formula: see text] of maximal subgroups of P such that [Formula: see text]. It is shown that if every member [Formula: see text] of is either S-quasinormally embedded or C-normal in G, then G is p-nilpotent. As its applications, some further results are obtained.

scholarly journals Towards a classification of rigid product quotient varieties of Kodaira dimension 0

2021 ◽  
Author(s):  
Ingrid Bauer ◽  
Christian Gleissner
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Structure Theorem ◽  
Complete Classification ◽  
Kodaira Dimension ◽  
The Other ◽  
Diagonal Action ◽  
Quotient Varieties ◽  
A Finite Group

AbstractIn this paper the authors study quotients of the product of elliptic curves by a rigid diagonal action of a finite group G. It is shown that only for $$G = {{\,\mathrm{He}\,}}(3), {\mathbb {Z}}_3^2$$ G = He ( 3 ) , Z 3 2 , and only for dimension $$\ge 4$$ ≥ 4 such an action can be free. A complete classification of the singular quotients in dimension 3 and the smooth quotients in dimension 4 is given. For the other finite groups a strong structure theorem for rigid quotients is proven.

Sign in / Sign up

Export Citation Format

Share Document