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...
10 KB (1,276 words) - 15:53, 13 July 2022
product Cartesian product of sets Direct product of groups Semidirect product Product of group subsets Wreath product Free product Zappa–Szép product...
2 KB (246 words) - 17:34, 11 July 2024
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...
284 bytes (62 words) - 00:45, 29 December 2020
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...
26 KB (2,932 words) - 23:03, 19 April 2024
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...
3 KB (396 words) - 23:32, 12 August 2023
Monoid (section Products and powers)
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...
35 KB (4,447 words) - 08:24, 16 July 2024
abelian group Free group Free product Generating set of a group Group cohomology Group extension Presentation of a group Product of group subsets Schur...
10 KB (800 words) - 20:17, 10 January 2024
Lexicographic order (redirect from Ordering of lexicographic type)
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...
23 KB (3,352 words) - 07:24, 16 November 2023
abstractly, one talks about the product in category theory, which formalizes these notions. Examples are the product of sets, groups (described below), rings...
16 KB (3,022 words) - 06:13, 4 July 2024
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...
11 KB (1,799 words) - 15:20, 12 May 2024
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...
1 KB (281 words) - 19:13, 26 April 2022
Haar measure (redirect from Unimodular group)
"invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This measure was introduced...
31 KB (5,360 words) - 23:32, 29 December 2023
Frattini's argument (category Lemmas in group theory)
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...
3 KB (554 words) - 19:19, 26 February 2024
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...
87 KB (9,321 words) - 09:58, 30 August 2024
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...
18 KB (2,309 words) - 19:40, 25 May 2024
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...
46 KB (5,637 words) - 12:41, 27 June 2024
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...
10 KB (1,467 words) - 09:22, 22 March 2024
Polish space (redirect from Polish group)
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...
12 KB (1,494 words) - 20:05, 11 August 2024
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...
74 KB (9,773 words) - 03:47, 6 September 2024
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}\...
25 KB (2,546 words) - 13:46, 21 June 2024
Centralizer and normalizer (redirect from Normalizer (group theory))
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...
14 KB (2,097 words) - 17:21, 1 June 2024
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...
34 KB (5,711 words) - 10:42, 17 August 2024
+ ) {\displaystyle (\mathbb {R} ,+)} . Different subsets of the same group can be generating subsets. For example, if p {\displaystyle p} and q {\displaystyle...
11 KB (1,746 words) - 14:56, 16 May 2023
Connected space (redirect from Main theorem of connectedness)
non-empty open subsets. Connectedness is one of the principal topological properties that are used to distinguish topological spaces. A subset of a topological...
26 KB (3,815 words) - 01:49, 4 February 2024
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...
8 KB (1,250 words) - 23:22, 2 December 2023
mathematics, specifically in group theory, the concept of a semidirect product is a generalization of a direct product. It is usually denoted with the...
30 KB (4,541 words) - 06:25, 10 August 2024
branch of mathematics, the Lebesgue measure, named after French mathematician Henri Lebesgue, is the standard way of assigning a measure to subsets of higher...
18 KB (2,641 words) - 20:13, 3 May 2024
product of representations is a tensor product of vector spaces underlying representations together with the factor-wise group action on the product....
16 KB (2,941 words) - 00:32, 28 June 2024
Semisimple Lie groups are Lie groups whose Lie algebra is a product of simple Lie algebras. They are central extensions of products of simple Lie groups. The identity...
64 KB (9,427 words) - 12:29, 18 August 2024