Groups : an introduction to ideas and methods of the theory of groups

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....

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Tác giả chính: Machì, Antonio, 19..-, mathématicien
Định dạng: Livre numérique
Ngôn ngữ:Anglais
Được phát hành: Milano : Springer Milan [20..].
Cham : Springer Nature
Phiên bản:1st ed. 2012.
Loạt:La Matematica per il 3+2
Những chủ đề:
Truy cập trực tuyến:Accès sur la plateforme de l'éditeur
Accès sur la plateforme Istex
Accès Université d'Orléans
Accès INSA CVL
Chú thích: Archives Springer e-books (Licence nationale)
Archives Springer e-books (Licence nationale)
Autres localisations: Voir dans le Sudoc
Edition sous un autre format:• Groups, Texte imprimé, 978-88-470-2420-5
• Groups, Texte imprimé, 9788847024229
• Groups, Texte imprimé, 9788847024205
• Groups, Texte imprimé, 9788847024229
• Groups, Texte imprimé, 9788847024205
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505 1 |a Normal Subgroups, Conjugation and Isomorphism Theorems Group Actions and Permutation Groups Generators and Relations Nilpotent Groups and Solvable Groups Representations Extensions and Cohomology Solution to the exercises. 
505 0 |a Normal Subgroups, Conjugation and Isomorphism Theorems -- Group Actions and Permutation Groups -- Generators and Relations -- Nilpotent Groups and Solvable Groups -- Representations -- Extensions and Cohomology -- Solution to the exercises 
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520 |a 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 
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