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...

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...

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

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...

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...

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

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

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...

In industry, product lifecycle management (PLM) is the process of managing the entire lifecycle of a product from its inception through the engineering...

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...

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...

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...

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

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...

thing to do: simply take as a basis of open sets to be the collection of all Cartesian products of open subsets from each factor: B = { U 1 × ⋯ × U n...

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

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...

{\displaystyle S} ). This example also shows that complete subsets (indeed, even compact subsets) of a non-Hausdorff space may fail to be closed (for example...

down to the unique interchangeable product regardless of manufacturer or package size. The code consists of seven subsets, each providing increasingly more...

mathematics, a group action of a group G {\displaystyle G} on a set S {\displaystyle S} is a group homomorphism from G {\displaystyle G} to some group (under...

of multiplication modulo a prime p {\displaystyle p} have order ⁠ p − 1 {\displaystyle p-1} ⁠. Any finite abelian group is isomorphic to a product of...

The Klein four-group is thus also the group generated by the symmetric difference as the binary operation on the subsets of a powerset of a set with two...

given finite group G to representation rings of a family X consisting of some subsets H of G. More precisely, for such a collection of subgroups, the...

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...

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

of subsets of G , {\displaystyle G,} compute certain probabilities, and integrate functions on G . {\displaystyle G.} A subgroup of a profinite group is...

element's centralizer. Similarly, we can define a group action of G {\displaystyle G} on the set of all subsets of G , {\displaystyle G,} by writing g ⋅ S :=...

those products cause. Although the word "product" has broad connotations, product liability as an area of law is traditionally limited to products in the...

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...

topology in AN, the Cartesian product of N copies of the adele ring. In this case, G ( A ) {\displaystyle G(A)} is a topological group. Historically the idèles...