profinite

profinite
Describing certain topological groups formed from finite groups

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  • Profinite group — In mathematics, profinite groups are topological groups that are in a certain sense assembled from finite groups; they share many properties with their finite quotients. Definition Formally, a profinite group is a Hausdorff, compact, and totally… …   Wikipedia

  • Profinite Gruppe — In der Mathematik ist eine proendliche oder profinite Gruppe eine topologische Gruppe G, die der inverse (projektive) Limes eines Systems von endlichen Gruppen ist. Dieser Limes wird in der Kategorie der topologischen Gruppen gebildet; hierbei… …   Deutsch Wikipedia

  • Absolute Galois group — In mathematics, the absolute Galois group GK of a field K is the Galois group of K sep over K , where K sep is a separable closure of K . Alternatively it is the group of all automorphisms of the algebraic closure of K that fix K . The absolute… …   Wikipedia

  • Residually finite group — In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every nontrivial element g in G there is a homomorphism h from G to a finite group, such that :h(g) eq 1.,There are a number of equivalent… …   Wikipedia

  • Embedding problem — In Galois theory, a branch of mathematics, the embedding problem is a generalization of the inverse Galois problem. Roughly speaking, it asks whether a given Galois extension can be embedded into a Galois extension in such a way that the… …   Wikipedia

  • Glossary of group theory — A group ( G , •) is a set G closed under a binary operation • satisfying the following 3 axioms:* Associativity : For all a , b and c in G , ( a • b ) • c = a • ( b • c ). * Identity element : There exists an e ∈ G such that for all a in G , e •… …   Wikipedia

  • Class formation — In mathematics, a class formation is a structure used to organize the various Galois groups and modules that appear in class field theory. They were invented by Emil Artin and John Tate. Contents 1 Definitions 2 Examples of class formations 3 The …   Wikipedia

  • Boolean algebras canonically defined — Boolean algebras have been formally defined variously as a kind of lattice and as a kind of ring. This article presents them more neutrally but equally formally as simply the models of the equational theory of two values, and observes the… …   Wikipedia

  • Field arithmetic — In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a ql|field (mathematics)|field and its absolute Galois group.It is an interdisciplinary subject as it uses tools from algebraic number… …   Wikipedia

  • Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

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