coset Definition
a subset of a group that is obtained by multiplying all the elements of a given subset by a particular element of the group.
Using coset: Examples
Take a moment to familiarize yourself with how "coset" can be used in various situations through the following examples!
Example
The cosets of a subgroup in a group form a partition of the group.
Example
The left coset of a subgroup H in a group G is the set {gh : h ∈ H} for some fixed g ∈ G.
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Summary: coset in Brief
A 'coset' [ˈkɑːzɛt] is a subset of a group that is obtained by multiplying all the elements of a given subset by a particular element of the group. The cosets of a subgroup in a group form a partition of the group, and the left coset of a subgroup H in a group G is the set {gh : h ∈ H} for some fixed g ∈ G.
