In the area of abstract algebra known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group, having order
808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000
= 246 · 320 · 59 · 76 · 112 · 133 · 17 · 19 · 23 · 29 · 31 · 41 · 47 · 59 · 71
≈ 8×1053.
Jacques Tits was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric.
In mathematics, more specifically in group theory, a group is said to be perfect if it equals its own commutator subgroup, or equivalently, if the group has no non-trivial abelian quotients. In symbols, a perfect group is one such that G(1) = G, or equivalently one such that Gab = {1}.
Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups can act non-trivially.
Grigory Aleksandrovich Margulis is a Russian-American mathematician known for his work on lattices in Lie groups, and the introduction of methods from ergodic theory into diophantine approximation. He was awarded a Fields Medal in 1978, a Wolf Prize in Mathematics in 2005, and an Abel Prize in 2020, becoming the fifth mathematician to receive the three prizes. In 1991, he joined the faculty of Yale University, where he is currently the Erastus L. De Forest Professor of Mathematics.
In mathematics, the Steinberg representation, or Steinberg module or Steinberg character, denoted by St, is a particular linear representation of a reductive algebraic group over a finite field or local field, or a group with a BN-pair. It is analogous to the 1-dimensional sign representation ε of a Coxeter or Weyl group that takes all reflections to –1.
Cheryl Elisabeth Praeger is an Australian mathematician. Praeger received BSc (1969) and MSc degrees from the University of Queensland (1974), and a doctorate from the University of Oxford in 1973 under direction of Peter M. Neumann. She has published widely and has advised 27 PhD students. She is currently Emeritus Professor of Mathematics at the University of Western Australia. She is best known for her works in group theory, algebraic graph theory and combinatorial designs.
Daniel Segal is a British mathematician and a Professor of Mathematics at the University of Oxford. He specialises in algebra and group theory.
In mathematics, the Chevalley–Shephard–Todd theorem in invariant theory of finite groups states that the ring of invariants of a finite group acting on a complex vector space is a polynomial ring if and only if the group is generated by pseudoreflections. In the case of subgroups of the complex general linear group the theorem was first proved by G. C. Shephard and J. A. Todd who gave a case-by-case proof. Claude Chevalley soon afterwards gave a uniform proof. It has been extended to finite linear groups over an arbitrary field in the non-modular case by Jean-Pierre Serre.
John Robert Stallings Jr. was a mathematician known for his seminal contributions to geometric group theory and 3-manifold topology. Stallings was a Professor Emeritus in the Department of Mathematics at the University of California at Berkeley where he had been a faculty member since 1967. He published over 50 papers, predominantly in the areas of geometric group theory and the topology of 3-manifolds. Stallings' most important contributions include a proof, in a 1960 paper, of the Poincaré Conjecture in dimensions greater than six and a proof, in a 1971 paper, of the Stallings theorem about ends of groups.
Gopal Prasad is an Indian-American mathematician. His research interests span the fields of Lie groups, their discrete subgroups, algebraic groups, arithmetic groups, geometry of locally symmetric spaces, and representation theory of reductive p-adic groups.
Aner Shalev is a professor at the Einstein Institute of Mathematics at the Hebrew University of Jerusalem, and a writer.
Norman Linstead Biggs is a leading British mathematician focusing on discrete mathematics and in particular algebraic combinatorics.
In mathematical finite group theory, a rank 3 permutation group acts transitively on a set such that the stabilizer of a point has 3 orbits. The study of these groups was started by Higman. Several of the sporadic simple groups were discovered as rank 3 permutation groups.
Gary Michael Seitz was an American mathematician, a Fellow of the American Mathematical Society and a College of Arts and Sciences Distinguished Professor Emeritus in Mathematics at the University of Oregon. He received his Ph.D. from the University of Oregon in 1968, where his adviser was Charles W. Curtis. Seitz specialized in the study of algebraic and finite groups. Seitz was active in the effort to exploit the relationship between algebraic groups and the finite groups of Lie type, in order to study the structure and representations of groups in the latter class. Such information is important in its own right, but was also critical in the classification of the finite simple groups, a major achievement of 20th century mathematics. Seitz made contributions to the classification of finite simple groups, such as those containing standard subgroups of Lie type. Following the classification, he pioneered the study of the subgroup structure of simple algebraic groups, and as an application went a long way towards solving the maximal subgroup problem for finite groups. For this work he received the Creativity Award from the National Science Foundation in 1991.
In mathematics, the O'Nan–Scott theorem is one of the most influential theorems of permutation group theory; the classification of finite simple groups is what makes it so useful. Originally the theorem was about maximal subgroups of the symmetric group. It appeared as an appendix to a paper by Leonard Scott written for The Santa Cruz Conference on Finite Groups in 1979, with a footnote that Michael O'Nan had independently proved the same result. Michael Aschbacher and Scott later gave a corrected version of the statement of the theorem.
Michael Ernest O'Nan was an American mathematician, specializing in group theory.
Pham Huu Tiep is a Vietnamese American mathematician specializing in group theory and representation theory. He is currently a Joshua Barlaz Distinguished Professor of Mathematics at Rutgers University.
Jan Saxl was a Czech-British mathematician, and a professor at the University of Cambridge. He was known for his work in finite group theory, particularly on consequences of the classification of finite simple groups.
Eamonn Anthony O'Brien is a professor of mathematics at the University of Auckland, New Zealand, known for his work in computational group theory and p-groups.
