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.
〔数〕傍系，陪集
Example sentencesExamples
Recall that Heidi seemed to be under the impression that cosets could be defined ostensively.
This observation led him into the intricacies of group theory: notions of groups, normal subgroups, quotient groups, running products, and cosets.
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.
The procedure, today much used in computer implementations, enumerates the cosets of a subgroup of finite index in a finitely presented group.
Here it amounts to elementwise multiplication of the two cosets.
Definition of coset in US English:
coset
nounˈkōset
Mathematics
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.
〔数〕傍系，陪集
Example sentencesExamples
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.