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...

domain Extension of a polyhedron, in geometry Exterior algebra, Grassmann's theory of extension, in geometry Field extension, in Galois theory Group extension...

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...

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 mathematics, particularly in algebra, a field extension (denoted L / K {\displaystyle L/K} ) is a pair of fields K ⊆ L {\displaystyle K\subseteq L}...

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,...

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

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...

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)...

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...

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

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...

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...

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

the machine in their facility. The leg extension is an isolated exercise targeting one specific muscle group, the quadriceps. It should not be considered...

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...

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

{\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;...

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...

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

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...

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

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...

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

individuals or groups in defining and achieving their goals in rural communities in the USA. Extension agents are trained in the skills of extension, such as...

The University of California, Berkeley, Extension (UC Berkeley Extension) is the continuing education division of the University of California, Berkeley...

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...