Ever-Evolving Groups

Alexander Anatolievich Ivanov is a distinguished Russian mathematician. Born in 1958 in the city of Yaroslavl, he graduated with distinction from the Moscow Institute of Physics and Technology in 1981, where he also received his PhD in 1984. Since that year, he has worked as a senior researcher at the Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences. In 1990, Ivanov delivered a 45-minute invited lecture at the International Congress of Mathematicians in Kyoto, Japan. In 2000, he received a Doctor of Science degree from Moscow State University.Over the years, Professor Ivanov has held visiting and regular professorial positions at several leading universities worldwide, including the University of Chicago, the University of Michigan, the University of Cambridge, the University of Tokyo, the University of Melbourne, and Imperial College London. At the latter institution, he taught algebra courses for a quarter of a century, which formed the foundation of the present volume.Professor Ivanov has established numerous groundbreaking results in algebra, combinatorics, and geometry, including Ivanov’s diameter bound for distance-regular graphs, the Y-presentation for the Monster group, and the launch of Majorana theory. He has published over one hundred research papers, five monographs, three collections of papers, and organized a dozen memorable international conferences.Since September 2024, he is a Professor at the School of Mathematical Sciences, Hebei Normal University, People’s Republic of China.

• 1 Basic Group Theory.- 2 Permutation Groups.- 3 Locally Symmetric Graphs.- 4 Dual Polar Spaces.- 5 The Dickson Group 𝑮2(3).- 6 Graphs Which Are Locally Something.- 7 Petersen and Tilde Geometries.- 8 Locally Projective Graphs.- 9 Geometry of the Thompson Group.- 10 Pushing Up.- 11 Buekenhout–Fisher Geometry for the Monster.- 12 Moonshine and Majorana.