coset

Noun

coset (plural cosets)

1. 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.
   • 1970 [Addison Wesley], Frederick W. Byron, Robert W. Fuller, Mathematics of Classical and Quantum Physics, Volumes 1-2, Dover, 1992, page 597,
     Theorem 10.5. The collection consisting of an invariant subgroup H and all its distinct cosets is itself a group, called the factor group of G, usually...
   • 1982 [Stanley Thornes], Linda Bostock, Suzanne Chandler, C. Rourke, Further Pure Mathematics, Nelson Thornes, 2002 Reprint, page 614,
     In general, the coset in row x consists of all the elements xh as h runs through the various elements of H.