# Category:Examples of Cosets

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This category contains examples of Coset.

### Left Coset

The **left coset of $x$ modulo $H$**, or **left coset of $H$ by $x$**, is:

- $x \circ H = \set {y \in S: \exists h \in H: y = x \circ h}$

That is, it is the subset product with singleton:

- $x \circ H = \set x \circ H$

### Right Coset

The **right coset of $y$ modulo $H$**, or **right coset of $H$ by $y$**, is:

- $H \circ y = \set {x \in S: \exists h \in H: x = h \circ y}$

That is, it is the subset product with singleton:

- $H \circ y = H \circ \set y$

## Pages in category "Examples of Cosets"

The following 20 pages are in this category, out of 20 total.

### C

- Coset/Examples
- Coset/Examples/Dihedral Group D3/Cosets of Subgroup Generated by b
- Coset/Examples/Dihedral Group D3/Cosets of Subgroup Generated by b/Left Cosets
- Coset/Examples/Dihedral Group D3/Cosets of Subgroup Generated by b/Right Cosets
- Coset/Examples/Subgroup of Infinite Cyclic Group
- Coset/Examples/Symmetric Group on 3 Letters/Cosets of Alternating Subgroup
- Coset/Examples/Symmetry Group of Equilateral Triangle/Cosets of Reflection Subgroup
- Cosets of Positive Reals in Multiplicative Group of Complex Numbers

### D

- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by A
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by A/Left Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by A/Right Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by B, F
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by B, F/Left Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by B, F/Right Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by D
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by D/Left Cosets
- Dihedral Group D4/Matrix Representation/Formulation 2/Examples of Cosets/Subgroup Generated by D/Right Cosets
- Dihedral Group D4/Subgroups/Cosets/Subgroup Generated by b
- Dihedral Group D4/Subgroups/Cosets/Subgroup Generated by b/Left Cosets
- Dihedral Group D4/Subgroups/Cosets/Subgroup Generated by b/Right Cosets