Minimal permutation representations of finite simple classical groups. Special linear, symplectic, and unitary groups

1993 ◽  
Vol 32 (3) ◽  
pp. 142-153 ◽  
Author(s):  
V. D. Mazurov
Keyword(s):  
Unitary Groups ◽  
Classical Groups ◽  
Special Linear

scholarly journals CHARACTER LEVELS AND CHARACTER BOUNDS

2020 ◽  
Vol 8 ◽  
Author(s):  
ROBERT M. GURALNICK ◽  
MICHAEL LARSEN ◽  
PHAM HUU TIEP
Keyword(s):  
Random Walks ◽  
Mixing Time ◽  
Upper Bounds ◽  
Unitary Groups ◽  
Covering Number ◽  
Classical Groups ◽  
Dual Pairs ◽  
Special Linear ◽  
Exponential Character ◽  
Finite Classical Groups

We develop the concept of character level for the complex irreducible characters of finite, general or special, linear and unitary groups. We give characterizations of the level of a character in terms of its Lusztig label and in terms of its degree. Then we prove explicit upper bounds for character values at elements with not-too-large centralizers and derive upper bounds on the covering number and mixing time of random walks corresponding to these conjugacy classes. We also characterize the level of the character in terms of certain dual pairs and prove explicit exponential character bounds for the character values, provided that the level is not too large. Several further applications are also provided. Related results for other finite classical groups are obtained in the sequel [Guralnick et al. ‘Character levels and character bounds for finite classical groups’, Preprint, 2019, arXiv:1904.08070] by different methods.

scholarly journals Non-Hurwitz Classical Groups

2007 ◽  
Vol 10 ◽  
pp. 21-82 ◽  
Author(s):  
R. Vincent ◽  
A.E. Zalesski
Keyword(s):  
Finite Fields ◽  
Unitary Groups ◽  
Classical Groups ◽  
Special Linear ◽  
Low Dimensional

AbstractIn previous work by Di Martino, Tamburini and Zalesski [Comm. Algebra28 (2000) 5383–5404] it is shown that certain low-dimensional classical groups over finite fields are not Hurwitz. In this paper the list is extended by adding the special linear and special unitary groups in dimensions 8.9,11.13. We also show that all groups Sp(n, q) are not Hurwitz forqeven andn= 6,8,12,16. In the range 11 <n< 32 many of these groups are shown to be non-Hurwitz. In addition, we observe that PSp(6, 3),PΩ±(8, 3k),PΩ±10k), Ω(11,3k), Ω±(14,3k), Ω±(16,7k), Ω(n, 7k) forn= 9,11,13, PSp(8, 7k) are not Hurwitz.

On Shalev's conjecture for type 𝐴𝑛 and 2𝐴𝑛

2019 ◽  
Vol 22 (4) ◽  
pp. 713-728 ◽  
Author(s):  
Alexey Galt ◽  
Amit Kulshrestha ◽  
Anupam Singh ◽  
Evgeny Vdovin
Keyword(s):  
Unitary Groups ◽  
Special Linear

AbstractIn the paper, we consider images of finite simple projective special linear and unitary groups under power words. In particular, we show that, if {G\simeq\operatorname{PSL}_{n}^{\varepsilon}(q)}, then, for every power word of type {x^{M}}, there exist constants c and N such that {\lvert\omega(G)\rvert>c\frac{\ln(n)\lvert G\rvert}{n}} whenever {\lvert G\rvert>N}.

scholarly journals The simple classical groups of dimension less than 6 which are (2,3)-generated

2015 ◽  
Vol 14 (10) ◽  
pp. 1550148 ◽  
Author(s):  
M. A. Pellegrini ◽  
M. C. Tamburini Bellani
Keyword(s):  
Soluble Group ◽  
Simple Groups ◽  
Linear Groups ◽  
Classical Groups ◽  
Special Linear ◽  
Special Linear Groups

In this paper, we determine the finite classical simple groups of dimension n = 3, 5 which are (2, 3)-generated (the cases n = 2, 4 are known). If n = 3, they are PSL 3(q), q ≠ 4, and PSU 3(q2), q2 ≠ 9, 25. If n = 5 they are PSL 5(q), for all q, and PSU 5(q2), q2 ≥ 9. Also, the soluble group PSU 3(4) is not (2, 3)-generated. We give explicit (2, 3)-generators of the linear preimages, in the special linear groups, of the (2, 3)-generated simple groups.

Conjugacy classes of small sizes in the linear and unitary groups

2013 ◽  
Vol 16 (6) ◽  
Author(s):  
Shawn T. Burkett ◽  
Hung Ngoc Nguyen
Keyword(s):  
Conjugacy Classes ◽  
Unitary Groups ◽  
General Linear ◽  
Linear Groups ◽  
Classical Groups ◽  
General Linear Groups ◽  
Finite Classical Groups

Abstract.Using the classical results of G. E. Wall on the parametrization and sizes of (conjugacy) classes of finite classical groups, we present some gap results for the class sizes of the general linear groups and general unitary groups as well as their variations. In particular, we identify the classes in

scholarly journals The number of regular semisimple classes of special linear and unitary groups

1998 ◽  
Vol 274 (1-3) ◽  
pp. 17-26 ◽  
Author(s):  
P. Fleischmann ◽  
I. Janiszczak ◽  
R. Knörr
Keyword(s):  
Unitary Groups ◽  
Special Linear
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