Finite simple group
= Finite simple group
A nontrivial <finite group> whose only <normal subgroups> are the <trivial group> and the whole group. A <cyclic group> of <prime number> order gives an abelian example; $A_5$ gives a nonabelian <alternating group> example. Finite versions of <classical groups> can produce further examples after taking suitable <subgroups> and quotients; small parameters require separate checks.