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...

generalization of the group axioms, this gives a notion of n-ary group. Mathematics portal List of group theory topics Order (group theory) Some authors include...

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...

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 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...

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

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...

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

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

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

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

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...

Look up Appendix:Glossary of order theory in Wiktionary, the free dictionary. This is a glossary of some terms used in various branches of mathematics...

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...

abelian group is a direct product of cyclic groups. Every cyclic group of prime order is a simple group, which cannot be broken down into smaller groups. In...

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

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

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...

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...

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...

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...

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

discontinuous (i.e., first-order) transitions. Although the theory has now been superseded by the renormalization group and scaling theory formulations, it remains...

such as Galois theory, invariant theory, the representation theory of Lie groups, and combinatorics. Cayley's theorem states that every group G {\displaystyle...

In mathematics, especially order theory, a partial order on a set is an arrangement such that, for certain pairs of elements, one precedes the other....

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...

Countryman line Order theory – Branch of mathematics Permutation – Mathematical version of an order change Prefix order – a downward total partial order Ranking –...

theory, the Dehornoy order is a left-invariant total order on the braid group, found by Patrick Dehornoy. Dehornoy's original discovery of the order on...