Suzuki Chain
The Suzuki chain or Suzuki tower is the following tower of rank 3 permutation groups from (Suzuki 1969), each of which is the point stabilizer of the next.
- G2(2) = U(3, 3) · 2 has a rank 3 action on 36 = 1 + 14 + 21 points with point stabilizer PSL(3, 2) · 2
- J2 · 2 has a rank 3 action on 100 = 1 + 36 + 63 points with point stabilizer G2(2)
- G2(4) · 2 has a rank 3 action on 416 = 1 + 100 + 315 points with point stabilizer J2 · 2
- Suz · 2 has a rank 3 action on 1782 = 1 + 416 + 1365 points with point stabilizer G2(4) · 2
Read more about this topic: Suzuki Sporadic Group
Famous quotes containing the word chain:
“How have I been able to live so long outside Nature without identifying myself with it? Everything lives, moves, everything corresponds; the magnetic rays, emanating either from myself or from others, cross the limitless chain of created things unimpeded; it is a transparent network that covers the world, and its slender threads communicate themselves by degrees to the planets and stars. Captive now upon earth, I commune with the chorus of the stars who share in my joys and sorrows.”
—Gérard De Nerval (1808–1855)