Orbit sizes and odd order composition factors of finite linear groups

2021 ◽  
pp. 103017
Author(s):  
Jinbao Li ◽  
Yong Yang
Keyword(s):  
Linear Groups ◽  
Odd Order ◽  
Composition Factors ◽  
Finite Linear

scholarly journals On the odd order composition factors of finite linear groups

2020 ◽  
Vol 23 (6) ◽  
pp. 1057-1068
Author(s):  
Alexander Betz ◽  
Max Chao-Haft ◽  
Ting Gong ◽  
Anthony Ter-Saakov ◽  
Yong Yang
Keyword(s):  
Linear Group ◽  
Linear Groups ◽  
Composition Series ◽  
Odd Order ◽  
Finite Linear Group ◽  
Composition Factors ◽  
Finite Linear

AbstractIn this paper, we study the product of orders of composition factors of odd order in a composition series of a finite linear group. First we generalize a result by Manz and Wolf about the order of solvable linear groups of odd order. Then we use this result to find bounds for the product of orders of composition factors of odd order in a composition series of a finite linear group.

scholarly journals Prime Power Representations of Finite Linear Groups II

1957 ◽  
Vol 9 ◽  
pp. 347-351 ◽  
Author(s):  
Robert Steinberg
Keyword(s):  
Lie Groups ◽  
Structural Properties ◽  
Lie Group ◽  
Prime Power ◽  
Linear Groups ◽  
Finite Linear

The aim of this paper is two-fold: first, to extend the results of (4) to the exceptional finite Lie groups recently discovered by Chevalley (1), and, secondly, to give a construction which works simultaneously for the groups An, Bn, Cn, Dn, En, F4 and G2 (in the usual Lie group notation), and which depends only on intrinsic structural properties of these groups.

scholarly journals Commutator Length of Finitely Generated Linear Groups

2008 ◽  
Vol 2008 ◽  
pp. 1-5
Author(s):  
Mahboubeh Alizadeh Sanati
Keyword(s):  
Finite Group ◽  
Upper Bound ◽  
Quadratic Polynomial ◽  
Linear Groups ◽  
Number Of Generators ◽  
Derived Subgroup ◽  
Finite Linear Group ◽  
Minimum Number ◽  
Commutator Length ◽  
Finite Linear

The commutator length “” of a group is the least natural number such that every element of the derived subgroup of is a product of commutators. We give an upper bound for when is a -generator nilpotent-by-abelian-by-finite group. Then, we give an upper bound for the commutator length of a soluble-by-finite linear group over that depends only on and the degree of linearity. For such a group , we prove that is less than , where is the minimum number of generators of (upper) triangular subgroup of and is a quadratic polynomial in . Finally we show that if is a soluble-by-finite group of Prüffer rank then , where is a quadratic polynomial in .

scholarly journals Quotient complete intersections of affine spaces by finite linear groups

1985 ◽  
Vol 98 ◽  
pp. 1-36 ◽  
Author(s):  
Haruhisa Nakajima
Keyword(s):  
Normal Subgroup ◽  
Affine Space ◽  
Finite Subgroup ◽  
Complete Intersections ◽  
Linear Groups ◽  
Coordinate Ring ◽  
Affine Spaces ◽  
Quotient Variety ◽  
Finite Linear ◽  
Complex Number Field

Let G be a finite subgroup of GLn(C) acting naturally on an affine space Cn of dimension n over the complex number field C and denote by Cn/G the quotient variety of Cn under this action of G. The purpose of this paper is to determine G completely such that Cn/G is a complete intersection (abbrev. CI.) i.e. its coordinate ring is a C.I. when n > 10. Our main result is (5.1). Since the subgroup N generated by all pseudo-reflections in G is a normal subgroup of G and Cn/G is obtained as the quotient variety of without loss of generality, we may assume that G is a subgroup of SLn(C) (cf. [6, 16, 24, 25]).

Prime Power Representations Of Finite Linear Groups

1956 ◽  
Vol 8 ◽  
pp. 580-591 ◽  
Author(s):  
Robert Steinberg
Keyword(s):  
Finite Groups ◽  
Symplectic Group ◽  
Prime Power ◽  
Projective Group ◽  
Linear Groups ◽  
Orthogonal Groups ◽  
Group 2 ◽  
Finite Linear ◽  
Two Parameter ◽  
Group 1

1. Introduction. There are five well-known, two-parameter families of simple finite groups: the unimodular projective group, the symplectic group,1 the unitary group,2 and the first and second orthogonal groups, each group acting on a vector space of a finite number of elements (2; 3).

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