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Author : T. Tsuzuku
Publisher : Cambridge University Press
Page : 344 pages
File Size : 49,7 Mb
Release : 1982-01-21
Category : Mathematics
ISBN : 9780521222426
A 1982 introduction to developments which had taken place in finite group theory related to finite geometries.
Author : Tosiro Tsuzuku
Publisher : Unknown
Page : 328 pages
File Size : 43,9 Mb
Release : 1976
Category : Electronic
ISBN : OCLC:636702961
Author : Peter Dembowski
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 54,7 Mb
Release : 1997
Category : Mathematics
ISBN : 3540617868
Peter Dembowski was born in Berlin on April 1, 1928. After studying mathematics at the University of Frankfurt of Main, he pursued his graduate studies at Brown Unviersity and the University of Illinois, mainly with R. Baer. Dembowski returned to Frankfurt in 1956. Shortly before his premature death in January 1971, he had been appointed to a chair at the University of Tuebingen. Dembowski taught at the universities of Frankfurt and Tuebingen and - as visiting Professor - in London (Queen Mary College), Rome, and Madison, WI. Dembowski's chief research interest lay in the connections between finite geometries and group theory. His book "Finite Geometries" brought together essentially all that was known at that time about finite geometrical structures, including key results of the author, in a unified and structured perspective. This book became a standard reference as soon as it appeared in 1968. It influenced the expansion of combinatorial geometric research, and left its trace also in neighbouring areas.
Author : Gyorgy Kiss,Tamas Szonyi
Publisher : CRC Press
Page : 274 pages
File Size : 48,9 Mb
Release : 2019-07-26
Category : Mathematics
ISBN : 9781351646383
Finite Geometries stands out from recent textbooks about the subject of finite geometries by having a broader scope. The authors thoroughly explain how the subject of finite geometries is a central part of discrete mathematics. The text is suitable for undergraduate and graduate courses. Additionally, it can be used as reference material on recent works. The authors examine how finite geometries’ applicable nature led to solutions of open problems in different fields, such as design theory, cryptography and extremal combinatorics. Other areas covered include proof techniques using polynomials in case of Desarguesian planes, and applications in extremal combinatorics, plus, recent material and developments. Features: Includes exercise sets for possible use in a graduate course Discusses applications to graph theory and extremal combinatorics Covers coding theory and cryptography Translated and revised text from the Hungarian published version
Author : William M. Kantor
Publisher : Unknown
Page : 184 pages
File Size : 43,9 Mb
Release : 1990
Category : Architecture
ISBN : UOM:39015018938798
The theory of buildings was introduced by J. Tits in order to focus on geometric and combinatorial aspects of simple groups of Lie type. Since then, the theory has blossomed into an extremely active field of mathematical research having deep connections with topics as diverse as algebraic groups, arithmetic groups, finite simple groups, and finite geometries, as well as with graph theory and other aspects of combinatorics. This volume is intended to provide an up-to-date survey of the theory of buildings with special emphasis on its interaction with related geometries. Experts in their respective fields provide coverage of such topics as the classification and construction of buildings, finite groups associated with building-like geometries, graphs and associated schemes, and more.
Author : Alexander Hulpke,Robert Liebler,Tim Penttila,Akos Seress
Publisher : Walter de Gruyter
Page : 287 pages
File Size : 45,9 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110199741
This volume is the proceedings of a conference on Finite Geometries, Groups, and Computation that took place on September 4-9, 2004, at Pingree Park, Colorado (a campus of Colorado State University). Not accidentally, the conference coincided with the 60th birthday of William Kantor, and the topics relate to his major research areas. Participants were encouraged to explore the deeper interplay between these fields. The survey papers by Kantor, O'Brien, and Penttila should serve to introduce both students and the broader mathematical community to these important topics and some of their connections while the volume as a whole gives an overview of current developments in these fields.
Author : M. Aschbacher,A.M. Cohen,W.M. Kantor
Publisher : Springer Science & Business Media
Page : 533 pages
File Size : 51,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400940178
The workshop was set up in order to stimulate the interaction between (finite and algebraic) geometries and groups. Five areas of concentrated research were chosen on which attention would be focused, namely: diagram geometries and chamber systems with transitive automorphism groups, geometries viewed as incidence systems, properties of finite groups of Lie type, geometries related to finite simple groups, and algebraic groups. The list of talks (cf. page iii) illustrates how these subjects were represented during the workshop. The contributions to these proceedings mainly belong to the first three areas; therefore, (i) diagram geometries and chamber systems with transitive automorphism groups, (ii) geometries viewed as incidence systems, and (iii) properties of finite groups of Lie type occur as section titles. The fourth and final section of these proceedings has been named graphs and groups; besides some graph theory, this encapsules most of the work related to finite simple groups that does not (explicitly) deal with diagram geometry. A few more words about the content: (i). Diagram geometries and chamber systems with transitive automorphism groups. As a consequence of Tits' seminal work on the subject, all finite buildings are known. But usually, in a situation where groups are to be characterized by certain data concerning subgroups, a lot less is known than the full parabolic picture corresponding to the building.
Author : Albrecht Beutelspacher,Frank de Clerck
Publisher : Cambridge University Press
Page : 428 pages
File Size : 54,5 Mb
Release : 1993
Category : Combinatorial analysis
ISBN : 0521448506
Included here are articles from many of the leading practitioners in the field, including, for the first time, several distinguished Russian mathematicians. Many of the papers contain important new results, and the growing use of computer algebra packages in this area is also demonstrated.
Author : F. Kárteszi
Publisher : Elsevier
Page : 281 pages
File Size : 50,9 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483278148
North-Holland Texts in Advanced Mathematics: Introduction to Finite Geometries focuses on the advancements in finite geometries, including mapping and combinatorics. The manuscript first offers information on the basic concepts on finite geometries and Galois geometries. Discussions focus on linear mapping of a given quadrangle onto another given quadrangle; point configurations of order 2 on a Galois plane of even order; canonical equation of curves of the second order on the Galois planes of even order; and set of collineations mapping a Galois plane onto itself. The text then ponders on geometrical configurations and nets, as well as pentagon theorem and the Desarguesian configuration, two pentagons inscribed into each other, and the concept of geometrical nets. The publication takes a look at combinatorial applications of finite geometries and combinatorics and finite geometries. Topics include generalizations of the Petersen graph, combinatorial extremal problem, and theorem of closure of the hyperbolic space. The book is a valuable source of data for readers interested in finite geometries.
Author : Peter Dembowski
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642620126
Peter Dembowski was born in Berlin on April 1, 1928. After studying mathematics at the University of Frankfurt of Main, he pursued his graduate studies at Brown Unviersity and the University of Illinois, mainly with R. Baer. Dembowski returned to Frankfurt in 1956. Shortly before his premature death in January 1971, he had been appointed to a chair at the University of Tuebingen. Dembowski taught at the universities of Frankfurt and Tuebingen and - as visiting Professor - in London (Queen Mary College), Rome, and Madison, WI. Dembowski's chief research interest lay in the connections between finite geometries and group theory. His book "Finite Geometries" brought together essentially all that was known at that time about finite geometrical structures, including key results of the author, in a unified and structured perspective. This book became a standard reference as soon as it appeared in 1968. It influenced the expansion of combinatorial geometric research, and left its trace also in neighbouring areas.
Author : N.S. Narasimha Sastry
Publisher : Springer Science & Business Media
Page : 348 pages
File Size : 41,9 Mb
Release : 2011-11-13
Category : Mathematics
ISBN : 9781461407096
This is the Proceedings of the ICM 2010 Satellite Conference on “Buildings, Finite Geometries and Groups” organized at the Indian Statistical Institute, Bangalore, during August 29 – 31, 2010. This is a collection of articles by some of the currently very active research workers in several areas related to finite simple groups, Chevalley groups and their generalizations: theory of buildings, finite incidence geometries, modular representations, Lie theory, etc. These articles reflect the current major trends in research in the geometric and combinatorial aspects of the study of these groups. The unique perspective the authors bring in their articles on the current developments and the major problems in their area is expected to be very useful to research mathematicians, graduate students and potential new entrants to these areas.
Author : Aart Blokhuis,James W.P. Hirschfeld,Dieter Jungnickel,Joseph A. Thas
Publisher : Springer Science & Business Media
Page : 366 pages
File Size : 51,6 Mb
Release : 2013-12-01
Category : Computers
ISBN : 9781461302834
When? These are the proceedings of Finite Geometries, the Fourth Isle of Thorns Conference, which took place from Sunday 16 to Friday 21 July, 2000. It was organised by the editors of this volume. The Third Conference in 1990 was published as Advances in Finite Geometries and Designs by Oxford University Press and the Second Conference in 1980 was published as Finite Geometries and Designs by Cambridge University Press. The main speakers were A. R. Calderbank, P. J. Cameron, C. E. Praeger, B. Schmidt, H. Van Maldeghem. There were 64 participants and 42 contributions, all listed at the end of the volume. Conference web site http://www. maths. susx. ac. uk/Staff/JWPH/ Why? This collection of 21 articles describes the latest research and current state of the art in the following inter-linked areas: • combinatorial structures in finite projective and affine spaces, also known as Galois geometries, in which combinatorial objects such as blocking sets, spreads and partial spreads, ovoids, arcs and caps, as well as curves and hypersurfaces, are all of interest; • geometric and algebraic coding theory; • finite groups and incidence geometries, as in polar spaces, gener alized polygons and diagram geometries; • algebraic and geometric design theory, in particular designs which have interesting symmetric properties and difference sets, which play an important role, because of their close connections to both Galois geometry and coding theory.
Author : Terrence Gagen,Terence M. Gagen
Publisher : Cambridge University Press
Page : 97 pages
File Size : 43,8 Mb
Release : 1976-04
Category : Mathematics
ISBN : 9780521210027
These notes derive from a course of lectures delivered at the University of Florida in Gainesville during 1971/2. Dr Gagen presents a simplified treatment of recent work by H. Bender on the classification of non-soluble groups with abelian Sylow 2-subgroups, together with some background material of wide interest. The book is for research students and specialists in group theory and allied subjects such as finite geometries.
Author : Steven T. Dougherty
Publisher : Springer Nature
Page : 374 pages
File Size : 43,5 Mb
Release : 2020-10-30
Category : Mathematics
ISBN : 9783030563950
This undergraduate textbook is suitable for introductory classes in combinatorics and related topics. The book covers a wide range of both pure and applied combinatorics, beginning with the very basics of enumeration and then going on to Latin squares, graphs and designs. The latter topic is closely related to finite geometry, which is developed in parallel. Applications to probability theory, algebra, coding theory, cryptology and combinatorial game theory comprise the later chapters. Throughout the book, examples and exercises illustrate the material, and the interrelations between the various topics is emphasized. Readers looking to take first steps toward the study of combinatorics, finite geometry, design theory, coding theory, or cryptology will find this book valuable. Essentially self-contained, there are very few prerequisites aside from some mathematical maturity, and the little algebra required is covered in the text. The book is also a valuable resource for anyone interested in discrete mathematics as it ties together a wide variety of topics.
Author : Bernhard Schmidt
Publisher : Springer
Page : 108 pages
File Size : 54,9 Mb
Release : 2004-10-14
Category : Mathematics
ISBN : 9783540457978
This monograph contributes to the existence theory of difference sets, cyclic irreducible codes and similar objects. The new method of field descent for cyclotomic integers of presribed absolute value is developed. Applications include the first substantial progress towards the Circulant Hadamard Matrix Conjecture and Ryser`s conjecture since decades. It is shown that there is no Barker sequence of length l with 13