On conjugacy classes of SL(2,q)

2009/04/02 by Edith Adan-Bante, Adan-Bante, Edith, John M. Harris +1
Mathematics · #20E45 #20G40 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR #msc:20E45 #msc:20G40

paper · pdf · doi:10.48550/arxiv.0904.0450

11 pages. Added references, corrected typos, improved presentation

arxiv created 2009/07/01 · arxiv updated 2009/12/01

Abstract

Let SL(2,q) be the group of 2X2 matrices with determinant one over a finite field F of size q. We prove that if q is even, then the product of any two noncentral conjugacy classes of SL(2,q) is the union of at least q-1 distinct conjugacy classes of SL(2,q). On the other hand, if q>3 is odd, then the product of any two noncentral conjugacy classes of SL(2,q) is the union of at least (q+3)/2 distinct conjugacy classes of SL(2,q).

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