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 mathematics, combinatorial group theory is the theory of free groups, and the concept of a presentation of a group by generators and relations. It...

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...

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

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

In mathematics, computational group theory is the study of groups by means of computers. It is concerned with designing and analysing algorithms and data...

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

In abstract algebra, the center of a group G is the set of elements that commute with every element of G. It is denoted Z(G), from German Zentrum, meaning...

Muted Group Theory (MGT) is a communication theory developed by cultural anthropologist Edwin Ardener and feminist scholar Shirley Ardener in 1975, that...

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

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...

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 of a group (also called...

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 group theory, Lagrange's theorem states that if H is a subgroup of any finite group G, then | H | {\displaystyle |H|} is...

In group theory, the normal closure of a subset S {\displaystyle S} of a group G {\displaystyle G} is the smallest normal subgroup of G {\displaystyle...

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

arise from group theoretical symmetries. In Lie's early work, the idea was to construct a theory of continuous groups, to complement the theory of discrete...

in quantum field theory. Stueckelberg and Petermann opened the field conceptually. They noted that renormalization exhibits a group of transformations...

Look up Appendix:Glossary of group theory in Wiktionary, the free dictionary. A group is a set together with an associative operation that admits an identity...

theory of groups is a part of mathematics which examines how groups act on given structures. Here the focus is in particular on operations of groups on...

foundations for combinatorial group theory. The following table lists some examples of presentations for commonly studied groups. Note that in each case there...

and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood...

discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential...

In 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...

representation theory of the symmetric group is a particular case of the representation theory of finite groups, for which a concrete and detailed theory can be...

theory — Galois theory — Game theory — Gauge theory — Graph theory — Group theory — Hodge theory — Homology theory — Homotopy theory — Ideal theory —...

such as groups, rings, and fields, based on the number of operations they use and the laws they follow. Universal algebra and category theory provide...

representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field...

are different definitions used in group theory and ring theory. The commutator of two elements, g and h, of a group G, is the element [g, h] = g−1h−1gh...

categories, and in group theory, where they are also known as sections, though this conflicts with a different meaning in category theory. So in the algebraic...