Journal ArticleDOI
Minimal characters of the finite classical groups
TLDR
In this article, it was shown that the number of projective complex characters of a finite simple group of Lie type over a finite field of order q and d(G(q)) is the minimal degree of faithful projective representations of G(q) is the same as that of a classical group.Abstract:
Let G(q) be a finite simple group of Lie type over a finite field of order q and d(G(q)) the minimal degree of faithful projective complex representations of G(q). For the case G(q) is a classical group we deter-mine the number of projective complex characters of G(q) of degree d(G(q)). In several cases we also determine the projective complex characters of the second and the third lowest degrees. As a corollary of these results we deduce the classification of quasi-simple irreducible complex linear groups of degree at most 2r r a prime divisor of the group order.read more
Citations
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Journal ArticleDOI
The Ore conjecture
TL;DR: In this paper, Liebeck and Shalev developed new strategies, combining character theoretic methods with other ingredients, and used them to establish the Ore conjecture, which states that every element of every finite non-abelian simple group is a commutator.
Journal ArticleDOI
Some Characterizations of the Weil Representations of the Symplectic and Unitary Groups
Pham Huu Tiep,A. E. Zalesskii +1 more
TL;DR: In this article, the authors characterize the Weil representations of G via their restriction to a standard subgroup and complete the determination of complex representations with specific minimal polynomials of certain elements.
Journal ArticleDOI
Character degrees and random walks in finite groups of Lie type
Martin W. Liebeck,Aner Shalev +1 more
TL;DR: In this paper, the authors studied the asymptotic behavior of the zeta function for simple groups of Lie type. And they also studied the properties of conjugacy classes.
Journal ArticleDOI
On the Minimal Degree of a Primitive Permutation Group
Robert M. Guralnick,Kay Magaard +1 more
TL;DR: In this article, the minimal degree of a primitive permutation group was improved and used to strengthen a result of Guralnick and Neubauer on generic covers of Riemann surfaces.
Journal ArticleDOI
The Waring problem for finite simple groups
TL;DR: The classical Waring problem deals with expressing every natural number as a sum of g(k) k-th powers as discussed by the authors, where the kth power word can be replaced by an arbitrary group word w 6 = 1, and the goal is to express group elements as short products of
References
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Book
Finite Groups of Lie Type: Conjugacy Classes and Complex Characters
TL;DR: The Steinberg Character as discussed by the authors is a character of Deligne-Lusztig, which is a generalization of the Steinberg character of Cuspidal Representations.
Book
The Subgroup Structure of the Finite Classical Groups
TL;DR: In this article, a unified treatment of the theory of geometric subgroups of the classical groups, introduced by Aschbacher, is presented, and the questions of maximality and conjugacy of these groups are answered.