Contributions to the Theory of Groups
Author: William Raymond Scott
Publisher:
Published: 1958
Total Pages: 129
ISBN-13:
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Author: William Raymond Scott
Publisher:
Published: 1958
Total Pages: 129
ISBN-13:
DOWNLOAD EBOOKAuthor: Kenneth I. Appel
Publisher: American Mathematical Soc.
Published: 1984
Total Pages: 534
ISBN-13: 0821850350
DOWNLOAD EBOOKContains five short articles about Roger Lyndon and his contributions to mathematics, as well as twenty-seven invited research papers in combinatorial group theory and closely related areas. Several of the articles featured in this work fall into subfields of combinatorial group theory, areas in which much of the initial work was done by Lyndon.
Author: John S. Rose
Publisher:
Published: 1975
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Hans Wussing
Publisher: Courier Corporation
Published: 2007-01-01
Total Pages: 338
ISBN-13: 0486458687
DOWNLOAD EBOOK"It is a pleasure to turn to Wussing's book, a sound presentation of history," declared the Bulletin of the American Mathematical Society. The author, Director of the Institute for the History of Medicine and Science at Leipzig University, traces the axiomatic formulation of the abstract notion of group. 1984 edition.
Author: University of Kansas. Department of Mathematics and Astronomy
Publisher:
Published: 1956
Total Pages: 142
ISBN-13:
DOWNLOAD EBOOKAuthor:
Publisher:
Published: 1956
Total Pages: 258
ISBN-13:
DOWNLOAD EBOOKAuthor: Frédérique Bassino
Publisher: Walter de Gruyter GmbH & Co KG
Published: 2020-06-08
Total Pages: 386
ISBN-13: 3110667029
DOWNLOAD EBOOKThis book shows new directions in group theory motivated by computer science. It reflects the transition from geometric group theory to group theory of the 21st century that has strong connections to computer science. Now that geometric group theory is drifting further and further away from group theory to geometry, it is natural to look for new tools and new directions in group theory which are present.
Author: Claude Chevalley
Publisher: Princeton University Press
Published: 2000-01-10
Total Pages: 234
ISBN-13: 9780691049908
DOWNLOAD EBOOKThis famous book was the first treatise on Lie groups in which a modern point of view was adopted systematically, namely, that a continuous group can be regarded as a global object. To develop this idea to its fullest extent, Chevalley incorporated a broad range of topics, such as the covering spaces of topological spaces, analytic manifolds, integration of complete systems of differential equations on a manifold, and the calculus of exterior differential forms. The book opens with a short description of the classical groups: unitary groups, orthogonal groups, symplectic groups, etc. These special groups are then used to illustrate the general properties of Lie groups, which are considered later. The general notion of a Lie group is defined and correlated with the algebraic notion of a Lie algebra; the subgroups, factor groups, and homomorphisms of Lie groups are studied by making use of the Lie algebra. The last chapter is concerned with the theory of compact groups, culminating in Peter-Weyl's theorem on the existence of representations. Given a compact group, it is shown how one can construct algebraically the corresponding Lie group with complex parameters which appears in the form of a certain algebraic variety (associated algebraic group). This construction is intimately related to the proof of the generalization given by Tannaka of Pontrjagin's duality theorem for Abelian groups. The continued importance of Lie groups in mathematics and theoretical physics make this an indispensable volume for researchers in both fields.
Author: William Raymond Scott
Publisher:
Published:
Total Pages:
ISBN-13:
DOWNLOAD EBOOKAuthor: Guo Wenbin
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 270
ISBN-13: 9401140545
DOWNLOAD EBOOKOne of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.