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...

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 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, 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...

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

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

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, Lagrange's theorem states that if H is a subgroup of any finite group G, then |H| is a divisor of |G|, i.e...

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...

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...

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

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...

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...

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...

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...

representations. This group is significant because special relativity together with quantum mechanics are the two physical theories that are most thoroughly...

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...

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

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

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

mathematics, Galois theory, originally introduced by Évariste Galois, provides a connection between field theory and group theory. This connection, the...

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

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...

to symmetry groups such as the Euclidean group and the group of projective transformations. In 1874 Lie introduced the theory of Lie groups, aiming for...

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...

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

split-complex numbers taking the transpose in a matrix ring. In group theory, an element of a group is an involution if it has order 2; that is, an involution...

group by an infinite-dimensional Hilbert space allows methods of analysis to be applied to the theory of groups. Furthermore, representation theory is...

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...