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 
, the trivial subgroup.
Every Abelian simple group is of the form 
, for some prime 
. The smallest non-Abelian simple group is 
, the alternating group on five elements. This group is of order 60.
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