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:
“What is the structure of government that will best guard against the precipitate counsels and factious combinations for unjust purposes, without a sacrifice of the fundamental principle of republicanism?”
—James Madison (1751–1836)
“I really do inhabit a system in which words are capable of shaking the entire structure of government, where words can prove mightier than ten military divisions.”
—Václav Havel (b. 1936)
“For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
—Ralph Waldo Emerson (1803–1882)
“Our manners have been corrupted by communication with the saints. Our hymn-books resound with a melodious cursing of God and enduring Him forever. One would say that even the prophets and redeemers had rather consoled the fears than confirmed the hopes of man. There is nowhere recorded a simple and irrepressible satisfaction with the gift of life, any memorable praise of God.”
—Henry David Thoreau (1817–1862)
“The awareness of the all-surpassing importance of social groups is now general property in America.”
—Johan Huizinga (1872–1945)