In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q {\displaystyle...

theory of extension, in geometry Field extension, in Galois theory Group extension, in abstract algebra and homological algebra Homotopy extension property...

mathematics, more specifically in topological groups, an extension of topological groups, or a topological extension, is a short exact sequence 0 → H → ı X →...

the Galois group of a certain type of field extension is a specific group associated with the field extension. The study of field extensions and their...

extension is a Galois extension whose Galois group is abelian. When the Galois group is also cyclic, the extension is also called a cyclic extension....

Central extension may refer to: Central Extension (Long Island Rail Road), a rail line Central extension (mathematics), a type of group extension This disambiguation...

in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. Equivalently,...

automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys...

local class field theory, the ramification groups are a filtration of the Galois group of a local field extension, which gives detailed information on the...

mathematics, the HNN extension is an important construction of combinatorial group theory. Introduced in a 1949 paper Embedding Theorems for Groups by Graham Higman...

In mathematics, particularly in algebra, a field extension is a pair of fields K ⊆ L {\displaystyle K\subseteq L} , such that the operations of K are...

that the first Ext group Ext1 classifies extensions of one module by another. In the special case of abelian groups, Ext was introduced by Reinhold Baer (1934)...

is an isolated exercise targeting one specific muscle group, the quadriceps. The leg extension machine was created by American fitness guru Jack LaLanne...

an algebra extension is the ring-theoretic equivalent of a group extension. Precisely, a ring extension of a ring R by an abelian group I is a pair (E...

In the theory of Lie groups, Lie algebras and their representation theory, a Lie algebra extension e is an enlargement of a given Lie algebra g by another...

did so the following year. Microsoft Edge added extension support in 2016. In 2015, a community group formed under the W3C to create a single standard...

totally ramified abelian extensions of a local field. It does this by considering the (formal) endomorphisms of the formal group, emulating the way in which...

algebraic extension to be a Galois extension. Bourbaki calls such an extension a quasi-Galois extension. For finite extensions, a normal extension is identical...

In mathematics, an algebraic extension is a field extension L/K such that every element of the larger field L is algebraic over the smaller field K; that...

a branch of algebra, an algebraic field extension E / F {\displaystyle E/F} is called a separable extension if for every α ∈ E {\displaystyle \alpha...

field theory, A radical extension of a field K {\displaystyle K} is a field extension obtained by a tower of field extensions, each generated by adjoining...

{\displaystyle G} is a group extension of G / N {\displaystyle G\,/\,N} by ⁠ N {\displaystyle N} ⁠. One could ask whether this extension is trivial or split;...

simple extension is a field extension that is generated by the adjunction of a single element, called a primitive element. Simple extensions are well...

group, which is a split extension and so trivial inside the H 2 {\displaystyle H^{2}} group. This is in fact the significance in group-theoretical terms of...

Trivial extension may refer to the following types of extensions: A trivial field extension A trivial group extension A trivial algebra extension This disambiguation...

(finite-dimensional) connected Lie groups via the operation of group extension. Many commonly encountered Lie groups are either simple or 'close' to being...

The Foothill Extension (formerly the Gold Line Foothill Extension) is a construction project extending the light rail A Line, a part of the Los Angeles...

Ore extension are called Ore polynomials. Ore extensions appear in several natural contexts, including skew and differential polynomial rings, group algebras...

well known: G is an extension of a finite group by either the infinite cyclic group or the infinite dihedral group. "Cyclic group", Encyclopedia of Mathematics...

Another way of putting this is that the Poincaré group is a group extension of the Lorentz group by a vector representation of it; it is sometimes dubbed...