Groups: An Introduction to Ideas and Methods of the Theory of Groups (UNITEXT / La Matematica per il 3+2) - Softcover

Machi, Antonio

Softcover

ISBN 10: 884702420X ISBN 13: 9788847024205

Verlag: Springer, 2012

Inhaltsangabe

Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder's program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.

Über diesen Titel

Über die Autorin bzw. den Autor

Laurea in Matematica, Roma 1965, Master of Science Università di Chicago 1968, professore visitatore Università di Bordeaux 1979-1981, Università Paris VII 1987-1993, e per soggiorni più brevi fino a tutt'oggi anche all'Università Paris VI e all'EHESS di Parigi. Membro dell'editorial board della rivista "European Journal of Combinatorics". Attualmente professore all'Università di Roma "La Sapienza

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Groups are a means of classification, via the group action on a set, but also the object of a classification. How many groups of a given type are there, and how can they be described? Hölder’s program for attacking this problem in the case of finite groups is a sort of leitmotiv throughout the text. Infinite groups are also considered, with particular attention to logical and decision problems. Abelian, nilpotent and solvable groups are studied both in the finite and infinite case. Permutation groups and are treated in detail; their relationship with Galois theory is often taken into account. The last two chapters deal with the representation theory of finite group and the cohomology theory of groups; the latter with special emphasis on the extension problem. The sections are followed by exercises; hints to the solution are given, and for most of them a complete solution is provided.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2012
• Sprache: Englisch
• ISBN 10: 884702420X
• ISBN 13: 9788847024205
• Einband: Taschenbuch
• Anzahl der Seiten: 396
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland