Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… … Wikipedia
Geometric group theory — is an area in mathematics devoted to the study of finitely generated groups via exploring the connections between algebraic properties of such groups and topological and geometric properties of spaces on which these groups act (that is, when the… … Wikipedia
Word (group theory) — 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 1 xzz , and y 1 zxx 1 yz 1 are words in the set { x , y , z }. Words play an important role … Wikipedia
Muted group theory — developed out of the cultural anthropology field, but more recently has been developed in communication mostly as a feminist and cross cultural theory. Muted group theory helps explain communication patterns and social representation of non… … Wikipedia
Order (group theory) — This article is about order in group theory. For order in other branches of mathematics, see Order (mathematics). For order in other disciplines, see Order. In group theory, a branch of mathematics, the term order is used in two closely related… … Wikipedia
Elementary group theory — In mathematics, a group is defined as a set G and a binary operation on G , called product and denoted by infix * . Product obeys the following rules (also called axioms). Let a , b , and c be arbitrary elements of G . Then: *A1, Closure. a * b… … Wikipedia
Transfer (group theory) — In mathematics, the transfer in group theory is a group homomorphism defined given a finite group G and a subgroup H , which goes from the abelianization of G to that of H .FormulationTo define the transfer, take coset representatives for the… … Wikipedia
Complement (group theory) — In mathematics, especially in the area of algebra known as group theory, a complement of a subgroup H in a group G is a subgroup K of G such that G = HK = { hk : h ∈ H and k ∈ K } and H ∩ K = {e}, that is, if every element of G has a unique… … Wikipedia
Component (group theory) — In mathematics, in the field of group theory, a component of a finite group is a quasisimple subnormal subgroup. Any two distinct components commute. The product of all the components is the layer of the group. For finite abelian (or nilpotent)… … Wikipedia
Block (group theory) — In mathematics and group theory, a block system for the action of a group G on a set X is a partition of X that is G invariant. In terms of the associated equivalence relation on X , G invariance means that : x ≡ y implies gx ≡ gy for all g in G… … Wikipedia
History of group theory — The history of group theory, a mathematical domain studying groups in their various forms, has evolved in various parallel threads. There are three historical roots of group theory: the theory of algebraic equations, number theory and geometry.… … Wikipedia