Structure of Finite Simple Groups
The famous theorem of Feit and Thompson states that every group of odd order is solvable. Therefore every finite simple group has even order unless it is cyclic of prime order.
The Schreier conjecture asserts that the group of outer automorphisms of every finite simple group is solvable. This can be proved using the classification theorem.
Read more about this topic: Simple Group
Famous quotes containing the words structure of, structure, finite, simple and/or groups:
“Women over fifty already form one of the largest groups in the population structure of the western world. As long as they like themselves, they will not be an oppressed minority. In order to like themselves they must reject trivialization by others of who and what they are. A grown woman should not have to masquerade as a girl in order to remain in the land of the living.”
—Germaine Greer (b. 1939)
“Man is more disposed to domination than freedom; and a structure of dominion not only gladdens the eye of the master who rears and protects it, but even its servants are uplifted by the thought that they are members of a whole, which rises high above the life and strength of single generations.”
—Karl Wilhelm Von Humboldt (1767–1835)
“We know then the existence and nature of the finite, because we also are finite and have extension. We know the existence of the infinite and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because he has neither extension nor limits.”
—Blaise Pascal (1623–1662)
“Armies, for the most part, are made up of men drawn from simple and peaceful lives. In time of war they suddenly find themselves living under conditions of violence, requiring new rules of conduct that are in direct contrast to the conditions they lived under as civilians. They learn to accept this to perform their duties as fighting men.”
—Gil Doud, U.S. screenwriter, and Jesse Hibbs. Walter Bedell Smith (Himself)
“... until both employers’ and workers’ groups assume responsibility for chastising their own recalcitrant children, they can vainly bay the moon about “ignorant” and “unfair” public criticism. Moreover, their failure to impose voluntarily upon their own groups codes of decency and honor will result in more and more necessity for government control.”
—Mary Barnett Gilson (1877–?)