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...

maximal order question can be examined at a local field level. This technique is applied in algebraic number theory and modular representation theory. Hurwitz...

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...

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

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

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...

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

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

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

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...

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

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 Although the theory has now been superseded by the renormalization group and scaling theory formulations, it remains...

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...

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...

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...

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...

Proponents of the theory believe these social bots were created intentionally to help manipulate algorithms and boost search results in order to manipulate...

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...

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...

Order theory is a branch of mathematics that studies various kinds of objects (often binary relations) that capture the intuitive notion of ordering, providing...

geometric group theory: one has the Cayley graph, which has a metric, called the word metric. These are also two resulting orders, the weak order and the...

renormalization group flow the field theory is conformally invariant. As the scale varies, it is as if one is decreasing (as RG is a semi-group and doesn't...

In the mathematical field of group theory, the transfer defines, given a group G and a subgroup H of finite index, a group homomorphism from G to the abelianization...

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....

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...

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...