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coset
This term is used exclusively within the specialized domain of abstract algebra, specifically group theory. It describes a specific partition of a group into disjoint sets, which is a foundational concept for understanding quotient groups and Lagrange's theorem. Because it is a technical mathematical term, it is never used in casual conversation or general literary contexts.
In mathematical discourse, the term is typically paired with the adjectives "left" or "right" to specify the side on which the group element is multiplied. While the concept is abstract, it functions as a standard countable noun within its academic register.
Meanings
Examples
The left coset of H in G is formed by multiplying each element of H by g on the left.
I wonder if this specific coset contains the identity element.
Two elements belong to the same coset if their difference is an element of the subgroup.
The set of all cosets forms a partition of the group.
Every coset of a subgroup has the same cardinality as the subgroup itself.
We can define the quotient group using these cosets as elements.
The intersection of two distinct cosets is always empty.
Let us pick a representative for each coset to simplify the calculation.
Let us pick a representative for each coset to simplify the calculation.