Download or read book The Subgroups of the Generalized Finite Modular Group written by Eliakim Hastings Moore and published by . This book was released on 1903 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Decennial Publications written by and published by . This book was released on 1904 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Modular Representation Theory of Finite Groups written by Peter Schneider and published by Springer Science & Business Media. This book was released on 2012-11-27 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representation theory studies maps from groups into the general linear group of a finite-dimensional vector space. For finite groups the theory comes in two distinct flavours. In the 'semisimple case' (for example over the field of complex numbers) one can use character theory to completely understand the representations. This by far is not sufficient when the characteristic of the field divides the order of the group. Modular Representation Theory of finite Groups comprises this second situation. Many additional tools are needed for this case. To mention some, there is the systematic use of Grothendieck groups leading to the Cartan matrix and the decomposition matrix of the group as well as Green's direct analysis of indecomposable representations. There is also the strategy of writing the category of all representations as the direct product of certain subcategories, the so-called 'blocks' of the group. Brauer's work then establishes correspondences between the blocks of the original group and blocks of certain subgroups the philosophy being that one is thereby reduced to a simpler situation. In particular, one can measure how nonsemisimple a category a block is by the size and structure of its so-called 'defect group'. All these concepts are made explicit for the example of the special linear group of two-by-two matrices over a finite prime field. Although the presentation is strongly biased towards the module theoretic point of view an attempt is made to strike a certain balance by also showing the reader the group theoretic approach. In particular, in the case of defect groups a detailed proof of the equivalence of the two approaches is given. This book aims to familiarize students at the masters level with the basic results, tools, and techniques of a beautiful and important algebraic theory. Some basic algebra together with the semisimple case are assumed to be known, although all facts to be used are restated (without proofs) in the text. Otherwise the book is entirely self-contained.

Download or read book The Decennial Publications written by University of Chicago and published by . This book was released on 1904 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Maximal Subgroups of the Low Dimensional Finite Classical Groups written by John N. Bray and published by Cambridge University Press. This book was released on 2013-07-25 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.

Download or read book The Decennial Publications of the University of Chicago written by University of Chicago and published by . This book was released on 1904 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Investigations Representing the Departments written by University of Chicago and published by . This book was released on 1903 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.

Download or read book Robert Steinberg Collected Papers written by Robert Steinberg and published by American Mathematical Soc.. This book was released on 1997 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of published papers by Robert Steinberg. It contains all of his published papers on group theory, including those on "special" representations (now called Steinberg representations), Coxeter groups, regular nilpotent elements and Galois cohomology. After each paper, there is a section, "Comments on the papers", that contains minor corrections and clarifications and explains how ideas and results have evolved and been used since they first appeared.

Download or read book The Velocity of Light written by Albert Abraham Michelson and published by . This book was released on 1904 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1899 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Annals of Mathematics written by and published by . This book was released on 1904 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The United States Catalog written by and published by . This book was released on 1906 with total page 2048 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometry and Collineation Groups of the Finite Projective Plane PG 2 22 written by Ulysses Grant Mitchell and published by . This book was released on 1910 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Generators and Relations in Groups and Geometries written by A. Barlotti and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann's work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char acterization are natural and plausible. They provoke the study of consequences of subsets of axioms which also yield natural geometries whose exploration is rewarding. Bachmann's central axiom is the three reflection theorem, showing that the number of reflections needed to express a motion is of great importance.

Download or read book Bulletin new Series of the American Mathematical Society written by and published by . This book was released on 1899 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Transactions of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1911 with total page 538 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monthly journal devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American Mathematical Society.