Structure
The Schreier conjecture asserts that Out(G) is always a solvable group when G is a finite simple group. This result is now known to be true as a corollary of the classification of finite simple groups, although no simpler proof is known.
Read more about this topic: Outer Automorphism Group
Famous quotes containing the word structure:
“Who says that fictions only and false hair
Become a verse? Is there in truth no beauty?
Is all good structure in a winding stair?
May no lines pass, except they do their duty
Not to a true, but painted chair?”
—George Herbert (1593–1633)
“When a house is tottering to its fall,
The strain lies heaviest on the weakest part,
One tiny crack throughout the structure spreads,
And its own weight soon brings it toppling down.”
—Ovid (Publius Ovidius Naso)
“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)