term, when referred to " has no nontrivial proper subgroups" refers to the only subgroups of being the trivial group and the group itself.

Properties

The trivial group is cyclic of order ; as such it may be denoted or . If the group operation is called addition, the trivial group is usually denoted by . If the group operation is called multiplication then can be a notation for the trivial group. Combining these leads to the trivial ring in which

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