Real and strongly real classes in SLn(q)

Abstract

We classify the real and strongly real conjugacy classes in GLn(q) and SLn(q). In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes.This paper is the first of two that together classify the real and strongly real classes in GLn(q), SLn(q), PGLn(q), PSLn(q), and all quasi-simple covers of PSLn(q).