mathematics, the order of a finite group is the number of its elements. If a group is not finite, one says that its order is infinite. The order of an element...

Order theory is a branch of mathematics that investigates the intuitive notion of order using binary relations. It provides a formal framework for describing...

In group theory, a word is any written product of group elements and their inverses. For example, if x, y and z are elements of a group G, then xy, z−1xzz...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

In mathematical order theory, an ideal is a special subset of a partially ordered set (poset). Although this term historically was derived from the notion...

representation theory (that is, through the representations of the group) and of computational group theory. A theory has been developed for finite groups, which...

algorithms in computational group theory include: the Schreier–Sims algorithm for finding the order of a permutation group the Todd–Coxeter algorithm and...

In mathematics, an order in the sense of ring theory is a subring O {\displaystyle {\mathcal {O}}} of a ring A {\displaystyle A} , such that A {\displaystyle...

examples of finite groups include cyclic groups and permutation groups. The study of finite groups has been an integral part of group theory since it arose...

Ordered set Order in Ramsey theory, uniform structures in consequence to critical set cardinality Order (group theory), the cardinality of a group or period...

The New World Order (NWO) is a term often used in conspiracy theories which hypothesize a secretly emerging totalitarian world government. The common...

In the mathematical area of order theory, every partially ordered set P gives rise to a dual (or opposite) partially ordered set which is often denoted...

In first-order logic, a first-order theory is given by a set of axioms in some language. This entry lists some of the more common examples used in model...

In the mathematical field of representation theory, group representations describe abstract groups in terms of bijective linear transformations of a vector...

abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally...

on embedding of elements of order 2 in finite groups called the Z* theorem, proved by George Glauberman using the theory developed by Brauer, was particularly...

The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical...

group of order n {\displaystyle n} is isomorphic to the additive group of Z/nZ, the integers modulo n {\displaystyle n} . Every cyclic group is an abelian...

In the mathematical area of order theory, completeness properties assert the existence of certain infima or suprema of a given partially ordered set (poset)...

Geometric group theory is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties...

In group theory, a branch of mathematics, a core is any of certain special normal subgroups of a group. The two most common types are the normal core...

mathematics, specifically group theory, Cauchy's theorem states that if G is a finite group and p is a prime number dividing the order of G (the number of elements...

mathematics students. In order to do so, it covers several other significant topics in graph theory, number theory, and group theory. It was written by Giuliana...

mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra:...

first-order logic. A theory about a topic, such as set theory, a theory for groups, or a formal theory of arithmetic, is usually a first-order logic together...

In group theory, an area of mathematics, an infinite group is a group whose underlying set contains an infinite number of elements. In other words, it...

In group theory, a branch of mathematics, a torsion group or a periodic group is a group in which every element has finite order. The exponent of such...

mathematics, and specifically in group theory, a non-abelian group, sometimes called a non-commutative group, is a group (G, ∗) in which there exists at...

Megaminx group has order 2, and the center of the Kilominx group is trivial. Quotienting out by the center of a group yields a sequence of groups called...

abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension...