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 threadbare trees, so poor and thin,
They are no wealthier than I;
But with as brave a core within
They rear their boughs to the October sky.
Poor knights they are which bravely wait
The charge of Winter’s cavalry,
Keeping a simple Roman state,
Discumbered of their Persian luxury.”
—Henry David Thoreau (1817–1862)
“Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
—Willa Cather (1873–1947)