Fibers of the square map in some finite groups of Lie type and an application

2024/03/25 by Panja, Saikat · 2 citations
#20D06 #20G40 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2403.17096

Abstract

Let G be one of the finite general linear, unitary, symplectic or orthogonal groups over finite fields of odd order. We find the cardinality of the fibers of the square map at a given generic element. Using this we find the number of real conjugacy classes of G. This is primarily achieved by leveraging a recent solution to Brauer's problem 14.

Cited by

• Dynamics of Word Maps on Groups and Polynomial Maps on Algebras
• Power maps on General Linear groups over finite principal ideal local rings of length two

Related

• The number of regular semisimple conjugacy classes in the finite classical groups
• Linear maps preserving fibers
• Squares of real conjugacy classes in finite groups
• Roots of identity in finite groups of Lie type
• On the number of real classes in the finite projective linear and unitary groups