Definition of coset in US English:



  • A set composed of all the products obtained by multiplying each element of a subgroup in turn by one particular element of the group containing the subgroup.

    • ‘This observation led him into the intricacies of group theory: notions of groups, normal subgroups, quotient groups, running products, and cosets.’
    • ‘Recall that Heidi seemed to be under the impression that cosets could be defined ostensively.’
    • ‘Here it amounts to elementwise multiplication of the two cosets.’
    • ‘The procedure, today much used in computer implementations, enumerates the cosets of a subgroup of finite index in a finitely presented group.’
    • ‘Although Euler's work is, of course, not stated in group theoretic terms he does provide an example of the decomposition of an abelian group into cosets of a subgroup.’