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:

    “The finite is annihilated in the presence of the infinite, and becomes a pure nothing. So our spirit before God, so our justice before divine justice.”
    —Blaise Pascal (1623–1662)

    “The world’s great day is growing late,
    Yet strange these fields that we have planted
    So long with crops of love and hate.”
    —Edwin Muir (1887–1959)