profinite group

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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

• Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

• Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

• Group cohomology — This article is about homology and cohomology of a group. For homology or cohomology groups of a space or other object, see Homology (mathematics). In abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well… …   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

• 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

• Compact group — In mathematics, a compact (topological, often understood) group is a topological group whose topology is compact. Compact groups are a natural generalisation of finite groups with the discrete topology and have properties that carry over in… …   Wikipedia

• Pro-p group — In mathematics, a pro p group (for some prime number p) is a profinite group G such that for any open normal subgroup the quotient group G / N is a p group. Note that, as profinite groups are compact, the open subgroup must be of finite index, so …   Wikipedia

• Topological group — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Finite group — In mathematics, a finite group is a group which has finitely many elements. Some aspects of the theory of finite groups were investigated in great depth in the twentieth century, in particular the local theory, and the theory of solvable groups… …   Wikipedia

• Galois group — In mathematics, a Galois group is a group associated with a certain type of field extension. The study of field extensions (and polynomials which give rise to them) via Galois groups is called Galois theory. The name is for Évariste Galois.For a… …   Wikipedia