Trivial group
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In mathematics, the trivial group is the group consisting of a single element, e. The group operation is e + e = e. The identity element is, of course, e, and the group is abelian; all these results being trivial, hence the name. The trivial group is often written as Z1 or just 0.
The trivial group should not be confused with the empty set (which has no elements and therefore, lacking an identity element, cannot be a group), though both play similar roles in their respective categories.
Every group contains a trivial subgroup.
