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 →...

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)...

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...

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...

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

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....

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,...

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...

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...

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...

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

Life extension is the concept of extending the human lifespan, either modestly through improvements in medicine or dramatically by increasing the maximum...

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...

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...

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...

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

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

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...

{\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;...

containing memory overlays had de facto standard extensions .OVL or .OVR (but also used numerical file extensions like .000, .001, etc. for subsequent files)...

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...

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...

radical extension of a field K is an extension of K that is obtained by adjoining a sequence of nth roots of elements. A simple radical extension is a simple...

The leg extension is a resistance weight training exercise that targets the quadriceps muscle (m. quadriceps femoris) in the legs. The exercise is done...

Agricultural extension is the application of scientific research and new knowledge to agricultural practices through farmer education. The field of 'extension' now...

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

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

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...