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Finite Geometry And Character Theory
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Book Synopsis Finite Geometry and Character Theory by : Alexander Pott
Download or read book Finite Geometry and Character Theory written by Alexander Pott and published by Springer. This book was released on 2006-11-14 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: Difference sets are of central interest in finite geometry and design theory. One of the main techniques to investigate abelian difference sets is a discrete version of the classical Fourier transform (i.e., character theory) in connection with algebraic number theory. This approach is described using only basic knowledge of algebra and algebraic number theory. It contains not only most of our present knowledge about abelian difference sets, but also gives applications of character theory to projective planes with quasiregular collineation groups. Therefore, the book is of interest both to geometers and mathematicians working on difference sets. Moreover, the Fourier transform is important in more applied branches of discrete mathematics such as coding theory and shift register sequences.
Book Synopsis Applications of character theory to problems in finite geometry by : Alexander Pott
Download or read book Applications of character theory to problems in finite geometry written by Alexander Pott and published by . This book was released on 1993 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Character Theory of Finite Groups by : Mark L. Lewis
Download or read book Character Theory of Finite Groups written by Mark L. Lewis and published by American Mathematical Soc.. This book was released on 2010-09-17 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a collection of papers from the Conference on Character Theory of Finite Groups, held at the Universitat de Valencia, Spain, on June 3-5, 2009, in honor of I. Martin Isaacs. The topics include permutation groups, character theory, p-groups, and group rings. The research articles feature new results on large normal abelian subgroups of p-groups, construction of certain wreath products, computing idempotents in group algebras of finite groups, and using dual pairs to study representations of cross characteristic in classical groups. The expository articles present results on vertex subgroups, measuring theorems in permutation groups, the development of super character theory, and open problems in character theory.
Book Synopsis The Character Theory of Finite Groups of Lie Type by : Meinolf Geck
Download or read book The Character Theory of Finite Groups of Lie Type written by Meinolf Geck and published by Cambridge University Press. This book was released on 2020-02-27 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Through the fundamental work of Deligne and Lusztig in the 1970s, further developed mainly by Lusztig, the character theory of reductive groups over finite fields has grown into a rich and vast area of mathematics. It incorporates tools and methods from algebraic geometry, topology, combinatorics and computer algebra, and has since evolved substantially. With this book, the authors meet the need for a contemporary treatment, complementing in core areas the well-established books of Carter and Digne–Michel. Focusing on applications in finite group theory, the authors gather previously scattered results and allow the reader to get to grips with the large body of literature available on the subject, covering topics such as regular embeddings, the Jordan decomposition of characters, d-Harish–Chandra theory and Lusztig induction for unipotent characters. Requiring only a modest background in algebraic geometry, this useful reference is suitable for beginning graduate students as well as researchers.
Book Synopsis Characters and Cyclotomic Fields in Finite Geometry by : Bernhard Schmidt
Download or read book Characters and Cyclotomic Fields in Finite Geometry written by Bernhard Schmidt and published by Springer. This book was released on 2004-10-13 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Character Theory of Finite Groups by : Irving Martin Isaacs
Download or read book Character Theory of Finite Groups written by Irving Martin Isaacs and published by . This book was released on 1976 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Finite Fields and Their Applications by : Pascale Charpin
Download or read book Finite Fields and Their Applications written by Pascale Charpin and published by Walter de Gruyter. This book was released on 2013-05-28 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
Book Synopsis Finite Geometries by : Catherine Anne Baker
Download or read book Finite Geometries written by Catherine Anne Baker and published by CRC Press. This book was released on 2020-10-15 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a compilation of the papers presented at the conference in Winnipeg on the subject of finite geometry in 1984. It covers different fields in finite geometry: classical finite geometry, the geometry of finite planes, geometric structures and the theory of translation planes.
Book Synopsis Finite Geometries by : Aart Blokhuis
Download or read book Finite Geometries written by Aart Blokhuis and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Representation Theory of Finite Groups by : Benjamin Steinberg
Download or read book Representation Theory of Finite Groups written by Benjamin Steinberg and published by Springer Science & Business Media. This book was released on 2011-10-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended to present group representation theory at a level accessible to mature undergraduate students and beginning graduate students. This is achieved by mainly keeping the required background to the level of undergraduate linear algebra, group theory and very basic ring theory. Module theory and Wedderburn theory, as well as tensor products, are deliberately avoided. Instead, we take an approach based on discrete Fourier Analysis. Applications to the spectral theory of graphs are given to help the student appreciate the usefulness of the subject. A number of exercises are included. This book is intended for a 3rd/4th undergraduate course or an introductory graduate course on group representation theory. However, it can also be used as a reference for workers in all areas of mathematics and statistics.
Book Synopsis Algebraic Geometry in Coding Theory and Cryptography by : Harald Niederreiter
Download or read book Algebraic Geometry in Coding Theory and Cryptography written by Harald Niederreiter and published by Princeton University Press. This book was released on 2009-09-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books
Book Synopsis Representation Theory of Finite Groups by : Martin Burrow
Download or read book Representation Theory of Finite Groups written by Martin Burrow and published by Courier Corporation. This book was released on 2014-05-05 with total page 210 pages. Available in PDF, EPUB and Kindle. Book excerpt: DIVConcise, graduate-level exposition covers representation theory of rings with identity, representation theory of finite groups, more. Exercises. Appendix. 1965 edition. /div
Download or read book Finite Geometries written by Johnson and published by CRC Press. This book was released on 1983-01-18 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Representation Theory of Finite Groups: Algebra and Arithmetic by : Steven H. Weintraub
Download or read book Representation Theory of Finite Groups: Algebra and Arithmetic written by Steven H. Weintraub and published by American Mathematical Soc.. This book was released on 2003 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: ``We explore widely in the valley of ordinary representations, and we take the reader over the mountain pass leading to the valley of modular representations, to a point from which (s)he can survey this valley, but we do not attempt to widely explore it. We hope the reader will be sufficiently fascinated by the scenery to further explore both valleys on his/her own.'' --from the Preface Representation theory plays important roles in geometry, algebra, analysis, and mathematical physics. In particular, representation theory has been one of the great tools in the study and classification of finite groups. There are some beautiful results that come from representation theory: Frobenius's Theorem, Burnside's Theorem, Artin's Theorem, Brauer's Theorem--all of which are covered in this textbook. Some seem uninspiring at first, but prove to be quite useful. Others are clearly deep from the outset. And when a group (finite or otherwise) acts on something else (as a set of symmetries, for example), one ends up with a natural representation of the group. This book is an introduction to the representation theory of finite groups from an algebraic point of view, regarding representations as modules over the group algebra. The approach is to develop the requisite algebra in reasonable generality and then to specialize it to the case of group representations. Methods and results particular to group representations, such as characters and induced representations, are developed in depth. Arithmetic comes into play when considering the field of definition of a representation, especially for subfields of the complex numbers. The book has an extensive development of the semisimple case, where the characteristic of the field is zero or is prime to the order of the group, and builds the foundations of the modular case, where the characteristic of the field divides the order of the group. The book assumes only the material of a standard graduate course in algebra. It is suitable as a text for a year-long graduate course. The subject is of interest to students of algebra, number theory and algebraic geometry. The systematic treatment presented here makes the book also valuable as a reference.
Book Synopsis Finite Geometry and Combinatorial Applications by : Simeon Ball
Download or read book Finite Geometry and Combinatorial Applications written by Simeon Ball and published by Cambridge University Press. This book was released on 2015-07-02 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A graduate-level introduction to finite geometry and its applications to other areas of combinatorics.
Book Synopsis Representation Theory by : William Fulton
Download or read book Representation Theory written by William Fulton and published by Springer Science & Business Media. This book was released on 1991 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introducing finite-dimensional representations of Lie groups and Lie algebras, this example-oriented book works from representation theory of finite groups, through Lie groups and Lie algrbras to the finite dimensional representations of the classical groups.
Book Synopsis Character Theory for the Odd Order Theorem by : Thomas Peterfalvi
Download or read book Character Theory for the Odd Order Theorem written by Thomas Peterfalvi and published by Cambridge University Press. This book was released on 2000-02-28 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The famous and important theorem of W. Feit and J. G. Thompson states that every group of odd order is solvable, and the proof of this has roughly two parts. The first part appeared in Bender and Glauberman's Local Analysis for the Odd Order Theorem which was number 188 in this series. This book provides the character-theoretic second part and thus completes the proof. All researchers in group theory should have a copy of this book in their library.
