Titlebook: A Course in the Theory of Groups; Derek J. S. Robinson Textbook 19931st edition Springer-Verlag New York, Inc. 1993 Abelian group.Finite.G

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Maligne Gezwellen (kwaadaardig)In this chapter we shall study ways in which a group may be decomposed into a set of groups each of which is in some sense of simpler type. This idea, the resolution of a single complex structure into a number of less complicated structures, is encountered in almost all branches of algebra.

tendinitis

https://doi.org/10.1007/978-90-313-6621-7The theory of abelian groups is a branch of group theory with a flavour all of its own. Indeed, as László Fuchs has remarked, there are few properties with a more decisive influence on group structure than commutativity.

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https://doi.org/10.1007/978-3-662-05621-9The aim of this chapter is to introduce the reader to the theory of representations of groups by linear transformations of a vector space or, equivalently, by matrices over a field. Aside from its intrinsic interest this theory has proved to be a most powerful tool for studying finite groups.

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John Baldessari,Liam Gillick,Beatrix RufThe subject of this chapter is one of the basic techniques of finite group theory, the transfer homomorphism. Since the kernel of this homomorphism has abelian quotient group, it is especially useful in the study of insoluble groups. It will be seen that this technique underlies many deep and important theorems about finite groups

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https://doi.org/10.1007/978-1-4684-0128-8Abelian group; Finite; Group theory; Permutation; algebra; automorphism; cohomology; finite group; group; gro