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:
“The real drawback to “the simple life” is that it is not simple. If you are living it, you positively can do nothing else. There is not time.”
—Katharine Fullerton Gerould (1879–1944)
“We often overestimate the influence of a peer group on our teenager. While the peer group is most influential in matters of taste and preference, we parents are most influential in more abiding matters of standards, beliefs, and values.”
—David Elkind (20th century)