coset
coset of a group G that possesses a subgroup H. A coset of G modulo H determined by the element x of G is a subset: x ◦ H = {x ◦ h  h ∈ H} H ◦ x = {h ◦ x  h ∈ H}
where ◦ is the dyadic operation defined on G. A subset of the former kind is called a left coset of G modulo H or a left coset of G in H; the latter is a right coset. In special cases x ◦ H = H ◦ x
for any x in G. Then H is called a normal subgroup of G. Any subgroup of an abelian group is a normal subgroup.
The cosets of G in H form a partition of the group G, each coset showing the same number of elements as H itself. These can be viewed as the equivalence classes of a left coset relation defined on the elements g_{1} and g_{2} of G as follows: g_{1} ρ g_{2} iff g_{1} ◦ H = g_{2} ◦ H
Similarly a right coset relation can be defined. When H is a normal subgroup the coset relation becomes a congruence relation.
Cosets have important applications in computer science, e.g. in the development of efficient codes needed in the transmission of information and in the design of fast adders.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"coset." A Dictionary of Computing. . Encyclopedia.com. 21 Aug. 2017 <http://www.encyclopedia.com>.
"coset." A Dictionary of Computing. . Encyclopedia.com. (August 21, 2017). http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/coset
"coset." A Dictionary of Computing. . Retrieved August 21, 2017 from Encyclopedia.com: http://www.encyclopedia.com/computing/dictionariesthesaurusespicturesandpressreleases/coset
coset
coset See CROSSSTRATIFICATION.
Cite this article
Pick a style below, and copy the text for your bibliography.

MLA

Chicago

APA
"coset." A Dictionary of Earth Sciences. . Encyclopedia.com. 21 Aug. 2017 <http://www.encyclopedia.com>.
"coset." A Dictionary of Earth Sciences. . Encyclopedia.com. (August 21, 2017). http://www.encyclopedia.com/science/dictionariesthesaurusespicturesandpressreleases/coset
"coset." A Dictionary of Earth Sciences. . Retrieved August 21, 2017 from Encyclopedia.com: http://www.encyclopedia.com/science/dictionariesthesaurusespicturesandpressreleases/coset