COSET

Etymology

Noun

coset (plural cosets)

(algebra, group theory) The set that results from applying a group's binary operation with a given fixed element of the group on each element of a given subgroup.

Usage notes

Mathematically, given a group $\(G\)$ with binary operation $\(\circ\)$ , element $\(g\in G\)$ and subgroup $\(H\subseteq G\)$ , the set $\(\left \{ g\circ h: h\in H \right \}\)$ , which also defines the left coset if $\(G\)$ is not assumed to be abelian.

The concept is relevant to the (mathematical) definitions of normal subgroup and quotient group.

Anagrams

• Coste, OTECs, ScotE, cotes, scote

Source: Wiktionary

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