Simple group

A simple group is a non-trivial group (i.e., a group with at least two elements) that has no non-trivial normal subgroups, i.e., none other than itself and $\{e\}$, the trivial subgroup.

Every Abelian simple group is of the form $\mathbb{Z}/p\mathbb{Z}$, for some prime $p$. The smallest non-Abelian simple group is $\mathfrak{A}_5$, the alternating group on five elements. This group is of order 60.

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See also