Everything about Coset
Disjoint, equal-size subsets of a group's underlying set
In mathematics, specifically group theory, a subgroup H of a group G may be used to decompose the underlying set of G into disjoint, equal-size subsets called cosets. There are left cosets and right cosets. Cosets have the same number of elements (cardinality) as does H. Furthermore, H itself is both a left coset and a right coset. The number of left cosets of H in G is equal to the number of right cosets of H in G. This common value is called the index of H in G and is usually denoted by [G : H]. Wikipedia →
🧠Start here: a 6-step reading path
- Read the overview: CosetA 5-minute orientation
- Skim a recent paper: Secure communication through reliable S-box design: A proposed approach using coset graphs and matrix operationsInfluential work since 2022
- Pick up a classic book: Extrait du Catalogue généralThe most-reprinted book on the subject
- Read the landmark paper: Virasoro algebras and coset space modelsCited 624 times
- Go sideways: Kernel (algebra)A closely related topic
- Go sideways: Double cosetA closely related topic
đź“– Definitions
Noun The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup.
🏆 Landmark papers (most cited)
Virasoro algebras and coset space models
Coset codes. II. Binary lattices and related codes
Coset codes. I. Introduction and geometrical classification
System Theory on Group Manifolds and Coset Spaces
Coset construction from functional integrals
Coset construction for extended Virasoro algebras
On holomorphic factorization of WZW and coset models
BRST quantization of the gauged WZW action and coset conformal field theories
🆕 Influential since 2022
Secure communication through reliable S-box design: A proposed approach using coset graphs and matrix operations
The fourth moment of Dirichlet L-functions along a coset and the Weyl bound
An international consensus study to identify “what” outcomes should be included in a core outcome set for endodontic treatments ( COSET ) for utilization in clinical practice and research
Fractionalization of coset non-invertible symmetry and exotic Hall conductance
The Schwinger-Keldysh coset construction
đź“š Books worth reading
- 📕Extrait du Catalogue généralMarcel Coset (Firm) · 1902
- 📕Woman's Institute Reference LibraryMary Brooks Picken · 1917
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đź”— Related topics
- Kernel (algebra) In algebra, the kernel of a homomorphism is the relation describing how elements in the domain of the homomorphism become related in the image. A homomorphism…
- Double coset In group theory, a field of mathematics, a double coset is a collection of group elements which are equivalent under the symmetries coming from two subgroups…
- Index of a subgroup In mathematics, specifically group theory, the index of a subgroup H in a group G is the number of left cosets of H in G, or equivalently, the number of…
- Quotient group In the branch of mathematics known as group theory, a quotient group or factor group is a group obtained by aggregating similar elements of a larger group…
- Subgroup In 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…
- Direct sum In mathematics, more specifically in algebra, the direct sum of a collection of abelian groups is an abelian group constructed by combining the given groups…
- Normal subgroup In abstract algebra, a normal subgroup (also known as an invariant subgroup or self-conjugate subgroup) is a subgroup that is invariant under conjugation…
- Topological group In mathematics, topological groups are groups and topological spaces at the same time, where the group operations are required to be continuous. This connects…