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...

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...

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

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...

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...

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

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...

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...

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...

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

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...

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...

is the sheaf associated to the pre-sheaf of the tensor products of the modules of sections over open subsets. In this setup, for example, one can define...

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

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...

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...

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...

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...

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...

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...

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

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}\...

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...

linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus,...

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, in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with...