Trivial Group
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High Quality Content by WIKIPEDIA articles! In mathematics, a trivial group is a group consisting of a single element. All such groups are isomorphic so one often speaks of the trivial group. The single element of the trivial group is the identity element so it usually denoted as such, 0, 1 or e depending on the context. The trivial group is often written as 0, 1, or e, using the same notation for the group and its sole element since there is little danger of confusion. If the group operation is denoted then it is defined by e e = e. The trivial group should not be confused with the empty set ...
High Quality Content by WIKIPEDIA articles! In mathematics, a trivial group is a group consisting of a single element. All such groups are isomorphic so one often speaks of the trivial group. The single element of the trivial group is the identity element so it usually denoted as such, 0, 1 or e depending on the context. The trivial group is often written as 0, 1, or e, using the same notation for the group and its sole element since there is little danger of confusion. If the group operation is denoted then it is defined by e e = e. 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). Given an arbitrary group G, the consisting of just the identity element is a trivial group and is a subgroup of G, it is called the trivial subgroup.
