Category:Definitions/Cosets

This category contains definitions related to Cosets.
Related results can be found in Category:Cosets.

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:

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