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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.’*

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