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Character Degrees and Random Walks in Finite Groups of Lie Type
Author(s) -
Liebeck Martin W.,
Shalev Aner
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611504014935
Subject(s) - mathematics , conjugacy class , random walk , type (biology) , combinatorics , character (mathematics) , classification of finite simple groups , group of lie type , permutation (music) , sporadic group , simple group , permutation group , simple lie group , mathematics subject classification , simple (philosophy) , lie group , pure mathematics , group theory , statistics , geometry , ecology , biology , philosophy , physics , epistemology , acoustics
For a finite group H , let Irr( H ) denote the set of irreducible characters of H , and define the ‘zeta function’ ζ H ( t ) = ∑ χ ∈ I r r ( H ) χ ( 1 ) − tfor real t > 0. We study the asymptotic behaviour of ζ H ( t ) for finite simple groups H of Lie type, and also of a corresponding zeta function defined in terms of conjugacy classes. Applications are given to the study of random walks on simple groups, and on base sizes of primitive permutation groups. 2000 Mathematics Subject Classification 20C33, 20P05, 60B15, 20D06.