scholarly journals Characters and Random Walks on Finite Classical Groups

1997 ◽  
Vol 129 (1) ◽  
pp. 46-72 ◽  
Author(s):  
David Gluck
Keyword(s):  
Random Walks ◽  
Classical Groups ◽  
Finite Classical Groups

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 Power series coefficients for probabilities in finite classical groups

2006 ◽  
Vol 305 (2) ◽  
pp. 1212-1237
Author(s):  
John R. Britnell ◽  
Jason Fulman
Keyword(s):  
Power Series ◽  
Classical Groups ◽  
Finite Classical Groups

scholarly journals The sylow 2-subgroups of the finite classical groups

1964 ◽  
Vol 1 (2) ◽  
pp. 139-151 ◽  
Author(s):  
Roger Carter ◽  
Paul Fong
Keyword(s):  
Classical Groups ◽  
Finite Classical Groups

RANDOM (r, s)-GENERATION OF FINITE CLASSICAL GROUPS

2002 ◽  
Vol 34 (2) ◽  
pp. 185-188 ◽  
Author(s):  
MARTIN W. LIEBECK ◽  
ANER SHALEV
Keyword(s):  
Classical Groups ◽  
Large Rank ◽  
Finite Classical Groups

A proof is given that for primes r, s, not both 2, and for finite simple classical groups G of sufficiently large rank, the probability that two randomly chosen elements in G of orders r and s generate G tends to 1 as |G| → ∞.

scholarly journals A geometric approach to Quillen’s conjecture

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Antonio Díaz Ramos ◽  
Nadia Mazza
Keyword(s):  
Finite Group ◽  
Prime Divisor ◽  
Geometric Approach ◽  
Classical Groups ◽  
Strong Version ◽  
Finite Classical Groups ◽  
A Finite Group

Abstract We introduce admissible collections for a finite group 𝐺 and use them to prove that most of the finite classical groups in non-defining characteristic satisfy the Quillen dimension at 𝑝 property, a strong version of Quillen’s conjecture, at a given odd prime divisor 𝑝 of | G | \lvert G\rvert . Compared to the methods in [M. Aschbacher and S. D. Smith, On Quillen’s conjecture for the 𝑝-groups complex, Ann. of Math. (2) 137 (1993), 3, 473–529], our techniques are simpler.

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