right cosets) are either disjoint or are identical as sets.

If the group operation is written additively, as is often the case when the group is abelian, the notation used changes to or , respectively.

The symbol G/H is sometimes used for the set of (left) cosets {gH : g an element of G} (see below for a extension to right cosets and double cosets). However, some authors (including Dummit & Foote and Rotman) reserve this notation specifically for representing the quotient group

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