Projective Linear Group - Finite Fields

Finite Fields

The projective special linear groups PSL(n,Fq) for a finite field Fq are often written as PSL(n,q) or Ln(q). They are finite simple groups whenever n is at least 2, with two exceptions: L2(2), which is isomorphic to S3, the symmetric group on 3 letters, and is solvable; and L2(3), which is isomorphic to A4, the alternating group on 4 letters, and is also solvable.

The special linear groups SL(n,q) are thus quasisimple: perfect central extensions of a simple group (unless and or 3).

Read more about this topic:  Projective Linear Group

Famous quotes containing the words finite and/or fields:

    “For it is only the finite that has wrought and suffered; the infinite lies stretched in smiling repose.”
    —Ralph Waldo Emerson (1803–1882)

    “Come up from the fields father, here’s a letter from our Pete,
    And come to the front door mother, here’s a letter from thy dear
    son.”
    —Walt Whitman (1819–1892)