Simple Group
A "Simple Group" is a type of mathematical group in the field of abstract algebra. It is defined as a nontrivial group that does not have any normal subgroups other than the trivial group and itself. This means that simple groups cannot be broken down into smaller, simpler groups through normal subgroup structures.
Simple groups play a crucial role in the classification of finite groups. The classification theorem states that every finite group can be built from simple groups, much like how numbers can be factored into prime numbers. Examples of simple groups include the alternating groups, denoted as A_n, and certain groups of prime order.