Meaning of coset in English:


Pronunciation /ˈkəʊsɛt/


  • 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.

    ‘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.’
    • ‘This observation led him into the intricacies of group theory: notions of groups, normal subgroups, quotient groups, running products, and cosets.’
    • ‘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.’
    • ‘Recall that Heidi seemed to be under the impression that cosets could be defined ostensively.’