scholarly journals The projective envelope of a cuspidal representation of a finite linear group

2014 ◽  
Vol 136 ◽  
pp. 354-374 ◽  
Author(s):  
David Paige
Keyword(s):  
Linear Group ◽  
Cuspidal Representation ◽  
Finite Linear Group ◽  
Finite Linear

The probability of generating a finite linear group

2004 ◽  
Vol 83 (5) ◽  
pp. 394-403
Author(s):  
Andrea Lucchini ◽  
Fiorenza Morini
Keyword(s):  
Linear Group ◽  
Finite Linear Group ◽  
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 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 Linear groups analogous to permutation groups

1963 ◽  
Vol 3 (2) ◽  
pp. 180-184 ◽  
Author(s):  
W. J. Wong
Keyword(s):  
Finite Group ◽  
Vector Space ◽  
Permutation Group ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Finite Linear Group ◽  
Singular Matrices ◽  
A Finite Group ◽  
Complex Coefficients ◽  
Finite Linear

If G is a finite linear group of degree n, that is, a finite group of automorphisms of an n-dimensional complex vector space (or, equivalently, a finite group of non-singular matrices of order n with complex coefficients), I shall say that G is a quasi-permutation group if the trace of every element of G is a non-negative rational integer. The reason for this terminology is that, if G is a permutation group of degree n, its elements, considered as acting on the elements of a basis of an n-dimensional complex vector space V, induce automorphisms of V forming a group isomorphic to G. The trace of the automorphism corresponding to an element x of G is equal to the number of letters left fixed by x, and so is a non-negative integer. Thus, a permutation group of degree n has a representation as a quasi-permutation group of degree n.

Finite Linear Groups of Prime Degree

1969 ◽  
Vol 21 ◽  
pp. 1025-1041 ◽  
Author(s):  
David B. Wales
Keyword(s):  
Finite Group ◽  
Linear Group ◽  
Irreducible Representations ◽  
Complex Representation ◽  
Linear Groups ◽  
Prime Degree ◽  
Long Time ◽  
A Finite Group ◽  
Finite Linear

If G is a finite group which has a faithful complex representation of degree nit is said to be a linear group of degree n. It is convenient to consider only unimodular irreducible representations. For n ≦ 4 these groups have been known for a long time. An account may be found in Blichfeldt's book (1). For n= 5 they were determined by Brauer in (4). In (4), many properties of linear groups of prime degree pwere determined for pa prime greater than or equal to 5.In a forthcoming series of papers these results will be extended and the linear groups of degree 7 determined. In the first paper, some general results on linear groups of degree p, p≧ 7, will be given. These results will later be applied to the prime p = 7.

scholarly journals The minimal degree of a faithful quasi-permutation representation of an abelian group

1997 ◽  
Vol 39 (1) ◽  
pp. 51-57 ◽  
Author(s):  
Houshang Behravesh
Keyword(s):  
Finite Group ◽  
Vector Space ◽  
Permutation Group ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Finite Linear Group ◽  
Singular Matrices ◽  
A Finite Group ◽  
Complex Coefficients ◽  
Finite Linear

Let G be a finite linear group of degree n; that is, a finite group of automorphisms of an n-dimensional complex vector space (or, equivalently, a finite group of non-singular matrices of order n with complex coefficients). We shall say that G is a quasi-permutation group if the trace of every element of G is a non-negative rational integer. The reason for this terminology is that, if G is a permutation group of degree n, its elements, considered as acting on the elements of a basis of an n -dimensional complex vector space V, induce automorphisms of V forming a group isomorphic to G. The trace of the automorphism corresponding to an element x of G is equal to the number of letters left fixed by x, and so is a non-negative integer. Thus, a permutation group of degree n has a representation as a quasi-permutation group of degree n. See [5].

On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

2020 ◽  
Vol 25 (4) ◽  
pp. 10-15
Author(s):  
Alexander Nikolaevich Rybalov
Keyword(s):  
Linear Group ◽  
Modular Group ◽  
Special Linear Group ◽  
Second Order ◽  
Integer Matrix ◽  
Subset Sum ◽  
Algorithmic Problems ◽  
Almost All ◽  
Subset Sum Problems ◽  
Generic Complexity

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.

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