In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, a normal subgroup and the quotient group, and the process can be repeated. If the group is finite, then eventually one arrives at uniquely determined simple groups by the Jordan–Hölder theorem.
Read more about Simple Group: Structure of Finite Simple Groups, History For Finite Simple Groups, Tests For Nonsimplicity
Famous quotes containing the words simple and/or group:
“He prayed more deeply for simple selflessness than he had ever prayed before—and, feeling an uprush of grace in the very intention, shed the night in his heart and called it light. And walking out of the little church he felt confirmed in not only the worth of his whispered prayer but in the realization, as well, that Christ had become man and not some bell-shaped Corinthian column with volutes for veins and a mandala of stone foliage for a heart.”
—Alexander Theroux (b. 1940)
“Laughing at someone else is an excellent way of learning how to laugh at oneself; and questioning what seem to be the absurd beliefs of another group is a good way of recognizing the potential absurdity of many of one’s own cherished beliefs.”
—Gore Vidal (b. 1925)