Simple group

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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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Simple group

From AoPSWiki

See also