Articles liés à The Theory of Groups

The Theory of Groups - Couverture souple

Zassenhaus, Hans J.

 
9780486409221: The Theory of Groups
Couverture souple
ISBN 10 : 0486409228 ISBN 13 : 9780486409221
Editeur : Dover Publications, 2011

Synopsis

Group theory represents one of the most fundamental elements of mathematics. Indispensable in nearly every branch of the field, concepts from the theory of groups also have important applications beyond mathematics, in such areas as quantum mechanics and crystallography. Hans J. Zassenhaus, a pioneer in the study of group theory, has designed this useful, well-written, graduate-level text to acquaint the reader with group-theoretic methods and to demonstrate their usefulness as tools in the solution of mathematical and physical problems. Starting with an exposition of the fundamental concepts of group theory, including an investigation of axioms, the calculus of complexes, and a theorem of Frobenius, the author moves on to a detailed investigation of the concept of homomorphic mapping, along with an examination of the structure and construction of composite groups from simple components. The elements of the theory of p-groups receive a coherent treatment, and the volume concludes with an explanation of a method by which solvable factor groups may be split off from a finite group. Many of the proofs in the text are shorter and more transparent than the usual, older ones, and a series of helpful appendixes presents material new to this edition. This material includes an account of the connections between lattice theory and group theory, and many advanced exercises illustrating both lattice-theoretical ideas and the extension of group-theoretical concepts to multiplicative domains.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

Group theory represents one of the most fundamental elements of mathematics. Indispensable in nearly every branch of the field, concepts from the theory of groups also have important applications beyond mathematics, in such areas as quantum mechanics and crystallography. Hans J. Zassenhaus, a pioneer in the study of group theory, has designed this useful, well-written, graduate-level text to acquaint the reader with group-theoretic methods and to demonstrate their usefulness as tools in the solution of mathematical and physical problems. Starting with an exposition of the fundamental concepts of group theory, including an investigation of axioms, the calculus of complexes, and a theorem of Frobenius, the author moves on to a detailed investigation of the concept of homomorphic mapping, along with an examination of the structure and construction of composite groups from simple components. The elements of the theory of p-groups receive a coherent treatment, and the volume concludes with an explanation of a method by which solvable factor groups may be split off from a finite group. Many of the proofs in the text are shorter and more transparent than the usual, older ones, and a series of helpful appendixes presents material new to this edition. This material includes an account of the connections between lattice theory and group theory, and many advanced exercises illustrating both lattice-theoretical ideas and the extension of group-theoretical concepts to multiplicative domains.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Dover Publications
Date d'édition
2011
Langue
anglais
ISBN 10 
0486409228
ISBN 13 
9780486409221
Reliure
Broché
Numéro d'édition
2
Nombre de pages
288
Coordonnées du fabricant
non disponible
Personne responsable
Soc. Agr. La Raia Ss
http://www.la-raia.it

Strada Monterotondo, 79
Novi Ligure
15067
Italie