Group theory

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. More precisely, let G be a group, and let H and K be subgroups. Let H act on G by left multiplication and let K act on G by right multiplication. For each x in G, the (H, K)-double coset of x is the set When H = K, this is called the H-double coset of x. Equivalently, HxK is the equivalence class of x under the equivalence relation x ~ y if and only if there exist h in H and k in K such that hxk = y. The set of all double cosets is denoted by (Wikipedia).

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Cosets generated by elements of cosets

What were to happen should we generate a left or right coset with an element of a coset? In this video I explore how we simply end up with the same coset.

From playlist Abstract algebra

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Coset deeper insights

A graphical representation of cosets using Caley tables, gives us a deeper insight. In this video we explore two cases. In the first, the element of G that creates the coset of the subgroup is in the subgroup and in the second, it is not.

From playlist Abstract algebra

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Proof: Cosets are Disjoint and Equal Size

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From playlist Group Theory

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From playlist Double and Triple Integrals

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From playlist Trigonometry

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From playlist COVARIANCE AND VARIANCE

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In this video I do an example problem calculating the right coset of a set, H, with an element from the symmetric group on four elements.

From playlist Abstract algebra

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Updated Version: https://youtu.be/4NznoskozDY Visit http://mathispower4u.wordpress.com/ for a categorized and searchable list of all videos.

From playlist Trigonometric Identities

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From playlist Double Angle Formulas

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Examples With Cosets -- Abstract Algebra Examples 9

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From playlist Abstract Algebra

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From playlist SMRI Algebra and Geometry Online

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Cosets -- Abstract Algebra video 9

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From playlist Abstract Algebra

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From playlist Diffusion Symmetry: A bridge between mathematics and physics

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From playlist Abstract Algebra

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From playlist Visual Group Theory

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From playlist École d'ÉtĂ© 2022 - Cohomology Geometry and Explicit Number Theory

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From playlist Visual Group Theory

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Abstract Algebra class April 13, 2021

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From playlist Super Lo-fi in class videos

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Related pages

Group action | Modular group | Functional analysis | Topological group | Index of a subgroup | Group (mathematics) | Bruhat decomposition | Permutation | Disjoint sets | Symmetric group | Bilinear map | Non-abelian group | Transposition (mathematics) | Disjoint union | Direct product of groups | Representation theory | Group ring | Equivalence class | Congruence subgroup | Gelfand pair | Free abelian group | Induced representation | Hecke algebra of a locally compact group | Integer | Hecke operator | Lagrange's theorem (group theory) | Mathematics | Set (mathematics) | Union (set theory) | Divisor | Group theory | Normal subgroup | Ring (mathematics) | Number theory | Convolution | Bijection | Integral | Equivalence relation | Subgroup | Commutator subgroup | Clifford–Klein form | Homogeneous space | Restricted representation | Coset | Permutation matrix | Abelian group | Commutative ring