Author: Timothy C. BurnessPublisher:
ISBN: 9781316439777
Category : Algebra
Languages : en
Pages : 346
Book Description
Classical Groups, Derangements and Primes
Author: Timothy C. BurnessPublisher:
ISBN: 9781316439777
Category : Algebra
Languages : en
Pages : 346
Book Description
Classical Groups, Derangements and Primes
Author: Timothy C. BurnessPublisher: Cambridge University Press
ISBN: 1107629446
Category : Mathematics
Languages : en
Pages : 365
Book Description
A graduate-level introduction to finite classical groups featuring a comprehensive account of the conjugacy and geometry of elements of prime order.
Classical Groups, Derangements and Primes
Author: Timothy C. BurnessPublisher:
ISBN: 9787560391892
Category : Algebra
Languages : en
Pages : 366
Book Description
The Spread of Almost Simple Classical Groups
Author: Scott HarperPublisher: Springer Nature
ISBN: 3030741001
Category : Mathematics
Languages : en
Pages : 154
Book Description
This monograph studies generating sets of almost simple classical groups, by bounding the spread of these groups. Guralnick and Kantor resolved a 1962 question of Steinberg by proving that in a finite simple group, every nontrivial element belongs to a generating pair. Groups with this property are said to be 3/2-generated. Breuer, Guralnick and Kantor conjectured that a finite group is 3/2-generated if and only if every proper quotient is cyclic. We prove a strong version of this conjecture for almost simple classical groups, by bounding the spread of these groups. This involves analysing the automorphisms, fixed point ratios and subgroup structure of almost simple classical groups, so the first half of this monograph is dedicated to these general topics. In particular, we give a general exposition of Shintani descent. This monograph will interest researchers in group generation, but the opening chapters also serve as a general introduction to the almost simple classical groups.
Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups
Author: Nick GillPublisher: Springer Nature
ISBN: 3030959562
Category : Mathematics
Languages : en
Pages : 221
Book Description
This book gives a proof of Cherlin’s conjecture for finite binary primitive permutation groups. Motivated by the part of model theory concerned with Lachlan’s theory of finite homogeneous relational structures, this conjecture proposes a classification of those finite primitive permutation groups that have relational complexity equal to 2. The first part gives a full introduction to Cherlin’s conjecture, including all the key ideas that have been used in the literature to prove some of its special cases. The second part completes the proof by dealing with primitive permutation groups that are almost simple with socle a group of Lie type. A great deal of material concerning properties of primitive permutation groups and almost simple groups is included, and new ideas are introduced. Addressing a hot topic which cuts across the disciplines of group theory, model theory and logic, this book will be of interest to a wide range of readers. It will be particularly useful for graduate students and researchers who need to work with simple groups of Lie type.
Amitsur Centennial Symposium
Author: Avinoam MannPublisher: American Mathematical Society, Bar-Ilan University
ISBN: 1470475553
Category : Mathematics
Languages : en
Pages : 322
Book Description
This volume contains the proceedings of the Amitsur Centennial Symposium, held from November 1–4, 2021, virtually and at the Israel Institute for Advanced Studies (IIAS), The Hebrew University of Jerusalem, Jerusalem, Israel. Shimshon Amitsur was a pioneer in several branches of algebra, the leading algebraist in Israel for several decades who contributed major theorems, inspiring results, useful observations, and enlightening tricks to many areas of the field. The fifteen papers included in the volume represent the broad impact of Amitsur's work on such areas as the theory of finite simple groups, algebraic groups, PI-algebras and growth of rings, quadratic forms and division algebras, torsors and Severi-Brauer surfaces, Hopf algebras and braces, invariants, automorphisms and derivations.
Groups, Combinatorics and Geometry
Author: Martin W. LiebeckPublisher: Cambridge University Press
ISBN: 0521406854
Category : Mathematics
Languages : en
Pages : 505
Book Description
This volume contains a collection of papers on the subject of the classification of finite simple groups.
Introduction to the Classical Groups
Author: Loren ButlerTopics in Graph Automorphisms and Reconstruction
Author: Josef LauriPublisher: Cambridge University Press
ISBN: 1316610446
Category : Mathematics
Languages : en
Pages : 207
Book Description
An in-depth coverage of selected areas of graph theory focusing on symmetry properties of graphs, ideal for beginners and specialists.
Expansion in Finite Simple Groups of Lie Type
Author: Terence TaoPublisher: American Mathematical Soc.
ISBN: 1470421968
Category : Mathematics
Languages : en
Pages : 319
Book Description
Expander graphs are an important tool in theoretical computer science, geometric group theory, probability, and number theory. Furthermore, the techniques used to rigorously establish the expansion property of a graph draw from such diverse areas of mathematics as representation theory, algebraic geometry, and arithmetic combinatorics. This text focuses on the latter topic in the important case of Cayley graphs on finite groups of Lie type, developing tools such as Kazhdan's property (T), quasirandomness, product estimates, escape from subvarieties, and the Balog-Szemerédi-Gowers lemma. Applications to the affine sieve of Bourgain, Gamburd, and Sarnak are also given. The material is largely self-contained, with additional sections on the general theory of expanders, spectral theory, Lie theory, and the Lang-Weil bound, as well as numerous exercises and other optional material.