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:
“All propaganda or popularization involves a putting of the complex into the simple, but such a move is instantly deconstructive. For if the complex can be put into the simple, then it cannot be as complex as it seemed in the first place; and if the simple can be an adequate medium of such complexity, then it cannot after all be as simple as all that.”
—Terry Eagleton (b. 1943)
“It is not God that is worshipped but the group or authority that claims to speak in His name. Sin becomes disobedience to authority not violation of integrity.”
—Sarvepalli, Sir Radhakrishnan (1888–1975)