one can define a product of group subsets in a natural way. If S and T are subsets of a group G, then their product is the subset of G defined by S T...

product Cartesian product of sets Direct product of groups Semidirect product Product of group subsets Wreath product Free product Zappa–Szép product...

a product of groups usually refers to a direct product of groups, but may also mean: semidirect product Product of group subsets wreath product free...

group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics. In the context of...

special type of complement in a Frobenius group. A complemented group is one where every subgroup has a complement. Product of group subsets David S. Dummit...

In the same way the power set of a group G is a monoid under the product of group subsets. Let S be a set. The set of all functions S → S forms a monoid...

abelian group Free group Free product Generating set of a group Group cohomology Group extension Presentation of a group Product of group subsets Schur...

an order on the subsets, which is also called the lexicographical order. In this context, one generally prefer to sort first the subsets by cardinality...

abstractly, one talks about the product in category theory, which formalizes these notions. Examples are the product of sets, groups (described below), rings...

Gross domestic product (GDP) is a monetary measure of the market value of all the final goods and services produced and rendered in a specific time period...

notion of quasirandom groups arises when considering subsets of groups for which no two elements in the subset have a product in the subset; such subsets are...

restricted product is a construction in the theory of topological groups. Let I {\displaystyle I} be an index set; S {\displaystyle S} a finite subset of I {\displaystyle...

"invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This measure was introduced...

normalizer of P {\displaystyle P} in G {\displaystyle G} , and N G ( P ) H {\displaystyle N_{G}(P)H} means the product of group subsets. The group P {\displaystyle...

of the free group. An arbitrary group G is called free if it is isomorphic to FS for some subset S of G, that is, if there is a subset S of G such that...

group as an abstract group, and to say that one has a group action of the abstract group that consists of performing the transformations of the group...

In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative...

group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation...

are Polish: closed subsets of a Polish space, open subsets of a Polish space, products and disjoint unions of countable families of Polish spaces, locally...

algebra operations, composition given by the product of group subsets, the converse by the inverse subset ( A − 1 = { a − 1 : a ∈ A } {\displaystyle A^{-1}=\{a^{-1}\...

+ ) {\displaystyle (\mathbb {R} ,+)} . Different subsets of the same group can be generating subsets. For example, if p {\displaystyle p} and q {\displaystyle...

direct product of groups, the element of H may change if the order of the factors is changed.) 2.  Outer semidirect product: if N and H are two groups, and...

normalizer of S are subgroups of G. Many techniques in group theory are based on studying the centralizers and normalizers of suitable subsets S. Suitably...

classical group, U(n) is the group that preserves the standard inner product on C n {\displaystyle \mathbb {C} ^{n}} . It is itself a subgroup of the general...

non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological...

Let G {\displaystyle G} be a group and K ≥ 1 {\displaystyle K\geq 1} ; for two subsets X , Y ⊂ G {\displaystyle X,Y\subset G} we denote by X ⋅ Y {\displaystyle...

product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group action on the product....

branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of higher...

mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. It is usually denoted with the...

groups list of simple Lie groups Representations of classical Lie groups Brauer algebra Infinite subsets of a compact space have an accumulation point and...