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I'm so confused. I know the trivial subgroup is identity itself.
1 Answer
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A trivial group is a group with only one element: $\{e\}$. Since all such groups are isomorphic, we often speak of the trivial group.
Every group clearly has the trivial group as a subgroup. A proper subgroup of a group $G$ is a subgroup that is not $G$ itself. If a group $G$ has no proper nontrivial subgroups, then its only subgroups are $G$ and $\{e\}$.
