Part I Cohomology of Finite Groups

Jürgen Neukirch
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Jürgen Neukirch: University of Regensburg

A chapter in Class Field Theory, 2013, pp 1-60 from Springer

Abstract: Abstract The cohomology of finite groups deals with a general situation that occurs frequently in different concrete forms. For example, if L|K is a finite Galois extension with Galois group G, then G acts on the multiplicative group L × of the extension field L. In the special case of an extension of finite algebraic number fields, G acts on the ideal group J of the extension field L. The theory of group extensions provides us with the following example: If G is an abstract finite group and A is a normal subgroup, then G acts on A via conjugation. In representation theory we study matrix groups G that act on a vector space. The basic notion underlying all these examples is that of a G-module. We will now present some general considerations about G-modules, some of which the reader may already know from the theory of modules over general rings.

Keywords: Abelian Group; Exact Sequence; Normal Subgroup; Finite Group; Cyclic Group (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/978-3-642-35437-3_1

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