Скачать или смотреть McKay Conjecture Math Couple Solves Group Theory Problem After 20 Years

We discuss the 20-year journey of mathematicians Britta Späth and Marc Cabanes in solving the McKay conjecture, a significant problem in group theory. The conjecture posits that key properties of a group can be determined by examining a much smaller subset, its Sylow normalizer. John McKay's initial observation of this coincidence sparked decades of research, including a crucial reformulation by Isaacs, Navarro, and Malle that paved the way for Späth and Cabanes. Their work focused on "groups of Lie type," overcoming considerable challenges. The proof, announced in 2023, simplifies the study of groups and hints at a deeper mathematical structure yet to be fully understood, although other researchers are beginning to explore possible explanations.