Definitions For Coset

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.

Derived terms

double coset left coset right coset

Translations

Estonian: kõrvalklass Finnish: sivuluokka Italian: classe laterale, f Polish: warstwa, f Portuguese: classe lateral, f Swedish: sidoklass, c

Etymology

co + set; apparently first used 1910 by american mathematician {{w + george abram miller}}.

Anagrams

Coste, OTECs, ScotE, cotes, scote