Real and strongly real classes in finite linear groups

2008/09/25 by Nick Gill, Anupam Singh, Gill, Nick +1
Mathematics · #20D06 #20E45 #20G40 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.0809.4412

openalex publication_date 2008/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify the real and strongly real conjugacy classes in GL_n(q), SL_n(q), PGL_n(q), PSL_n(q), and all quasi-simple covers of PSL_n(q). In each case we give a formula for the number of real, and the number of strongly real, conjugacy classes.

Related

• On the number of real classes in the finite projective linear and unitary groups
• Conjugate Real Classes in General Linear Groups
• Real Classes of Finite Special Unitary Groups
• Some problems about products of conjugacy classes in finite groups
• Real class sizes