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Catalogue Information
Field name	Details
Dewey Class	512
Title	Groups ([Ebook]) : An Introduction to Ideas and Methods of the Theory of Groups / by Antonio Machì
Author	Machì, Antonio
Other name(s)	SpringerLink (Online service)
Publication	Milano : Springer Milan
Publication	, 2012.
Physical Details	XIII, 371 pages : online resource.
Series	Unitext 2038-5714
ISBN	9788847024212
Summary Note	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? HÃ¶lderâs 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.:
Contents note	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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-88-470-2421-2
Links to Related Works	Subject References: Algebra . Commutative Rings and Algebras . Group theory . Group Theory and Generalizations . Mathematics . Authors: Machì, Antonio . Corporate Authors: SpringerLink (Online service) . Series: Unitext . Classification: 512 . 512 (DDC 23) .

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Groups: An Introduction to Ideas and Methods of the Theory of Groups

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