Elements with r-th roots in finite groups

2010/08/12 by Elaheh Khamseh, Mohammad Reza R. Moghaddam, Khamseh, Elaheh +6
Engineering · Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #graph theory and CDMA systems #math.GR #msc:20D60 #msc:20P05

paper · pdf · doi:10.48550/arxiv.1008.2055

7 pages; Fundamental revisions have been done

arxiv created 2012/06/19 · arxiv updated 2012/06/20

Abstract

The probability that a randomly chosen element of a finite group is an r--th root (for any integer r≥2) has been studied largely in case r=2. Certain techniques may be generalized for r>2 and here we find the exact value of this probability for projective special linear groups. A result of density is placed at the end, in order to show an analogy with the case r=2.

Related

• A probabilistic approach toward the finite general linear and unitary groups
• On real roots of polynomial systems of equations in the context of group theory
• On the distribution of the number of fixed vectors for the finite classical groups
• Derangements in finite classical groups and characteristic polynomials of random matrices
• On the probability of generating invariably a finite simple group