On Finite Groups Acting On Polygonal Graphs
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Fourier Analysis on Finite Groups and Applications
Author | : Audrey Terras |
Publisher | : Cambridge University Press |
Total Pages | : 456 |
Release | : 1999-03-28 |
Genre | : Mathematics |
ISBN | : 9780521457187 |
It examines the theory of finite groups in a manner that is both accessible to the beginner and suitable for graduate research.
Finite Groups and Finite Geometries
Author | : T. Tsuzuku |
Publisher | : Cambridge University Press |
Total Pages | : 344 |
Release | : 1982-01-21 |
Genre | : Mathematics |
ISBN | : 0521222427 |
A 1982 introduction to developments which had taken place in finite group theory related to finite geometries.
Proceedings of the Conference on Finite Groups
Author | : William R. Scott |
Publisher | : Academic Press |
Total Pages | : 580 |
Release | : 2014-05-10 |
Genre | : Mathematics |
ISBN | : 1483261085 |
Proceedings of the Conference on Finite Groups provides information pertinent to the fundamental aspects of finite group theory. This book presents the problem of characterizing simple groups in terms of the local structure of a group. Organized into five parts encompassing 43 chapters, this book begins with an overview of the characterization of the Chevalley groups over fields of odd order and indicates the role of this characterization in the theory of component type groups. This text then examines the structure as well as the representations of specific simple groups. Other chapters consider the general theory of representations and characters of finite groups. This book discusses as well permutation groups and the connection between group theory and geometry. The final chapter deals with finite solvable groups as well as the theory of formations. This book is a valuable resource for mathematicians, graduate students, and research workers.
Generalized Polygons
Author | : Hendrik Van Maldeghem |
Publisher | : Springer Science & Business Media |
Total Pages | : 511 |
Release | : 2012-01-03 |
Genre | : Mathematics |
ISBN | : 3034802714 |
Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.
Applying the Classification of Finite Simple Groups
Author | : Stephen D. Smith |
Publisher | : American Mathematical Soc. |
Total Pages | : 248 |
Release | : 2018-04-30 |
Genre | : Mathematics |
ISBN | : 1470442914 |
Classification of Finite Simple Groups (CFSG) is a major project involving work by hundreds of researchers. The work was largely completed by about 1983, although final publication of the “quasithin” part was delayed until 2004. Since the 1980s, CFSG has had a huge influence on work in finite group theory and in many adjacent fields of mathematics. This book attempts to survey and sample a number of such topics from the very large and increasingly active research area of applications of CFSG. The book is based on the author's lectures at the September 2015 Venice Summer School on Finite Groups. With about 50 exercises from original lectures, it can serve as a second-year graduate course for students who have had first-year graduate algebra. It may be of particular interest to students looking for a dissertation topic around group theory. It can also be useful as an introduction and basic reference; in addition, it indicates fuller citations to the appropriate literature for readers who wish to go on to more detailed sources.
Hyperbolically Embedded Subgroups and Rotating Families in Groups Acting on Hyperbolic Spaces
Author | : F. Dahmani |
Publisher | : American Mathematical Soc. |
Total Pages | : 164 |
Release | : 2017-01-18 |
Genre | : Mathematics |
ISBN | : 1470421941 |
he authors introduce and study the notions of hyperbolically embedded and very rotating families of subgroups. The former notion can be thought of as a generalization of the peripheral structure of a relatively hyperbolic group, while the latter one provides a natural framework for developing a geometric version of small cancellation theory. Examples of such families naturally occur in groups acting on hyperbolic spaces including hyperbolic and relatively hyperbolic groups, mapping class groups, , and the Cremona group. Other examples can be found among groups acting geometrically on spaces, fundamental groups of graphs of groups, etc. The authors obtain a number of general results about rotating families and hyperbolically embedded subgroups; although their technique applies to a wide class of groups, it is capable of producing new results even for well-studied particular classes. For instance, the authors solve two open problems about mapping class groups, and obtain some results which are new even for relatively hyperbolic groups.
Geometry of Sporadic Groups: Volume 1, Petersen and Tilde Geometries
Author | : A. A. Ivanov |
Publisher | : Cambridge University Press |
Total Pages | : 434 |
Release | : 1999-06-17 |
Genre | : Mathematics |
ISBN | : 0521413621 |
Important monograph on finite group theory.