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 $\backslash (G\backslash )$ with binary operation $\backslash (\backslash circ\backslash )$, element $\backslash (g\backslash in\; G\backslash )$ and subgroup $\backslash (H\backslash subseteq\; G\backslash )$, the set $\backslash (\backslash left\; \backslash \{\; g\backslash circ\; h:\; h\backslash in\; H\; \backslash right\; \backslash \}\backslash )$, which also defines the left coset if $\backslash (G\backslash )$ 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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