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The Suzuki groups Sz(q) or 2 B 2 (q) are simple for n≥1. The group Sz(2) is solvable and is the Frobenius group of order 20. The Suzuki groups Sz(q) have orders q 2 (q 2 +1)(q−1). These groups have orders divisible by 5, but not by 3. The Schur multiplier is trivial for n>1, Klein 4-group for n=1, i. e. Sz(8).
The Suzuki sporadic group, Suz or Sz is a sporadic simple group of order 2 13 · 3 7 · 5 2 · 7 · 11 · 13 = 448,345,497,600 discovered by Suzuki in 1969 One of an infinite family of Suzuki groups of Lie type discovered by Suzuki
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. G 2 (2) = U(3, 3) · 2 has a rank 3 action on 36 = 1 + 14 + 21 points with point stabilizer PSL(3, 2) · 2; J 2 · 2 has a rank 3 action on 100 = 1 + 36 + 63 points with point stabilizer G 2 (2)
Outer automorphism group: 1⋅f⋅1, where f = 2n + 1. Other names: Suz(2 2n+1), Sz(2 2n+1). Isomorphisms: 2 B 2 (2) is the Frobenius group of order 20. Remarks: Suzuki group are Zassenhaus groups acting on sets of size (2 2n+1) 2 + 1, and have 4-dimensional representations over the field with 2 2n+1 elements. They are the only non-cyclic ...
The simple N-groups were classified by Thompson (1968, 1970, 1971, 1973, 1974, 1974b) in a series of 6 papers totaling about 400 pages.The simple N-groups consist of the special linear groups PSL 2 (q), PSL 3 (3), the Suzuki groups Sz(2 2n+1), the unitary group U 3 (3), the alternating group A 7, the Mathieu group M 11, and the Tits group.
A notable achievement was his discovery in 1960 of the Suzuki groups, an infinite family of the only non-abelian simple groups whose order is not divisible by 3. The smallest, of order 29120, was the first simple group of order less than 1 million to be discovered since Dickson's list of 1900.
In mathematics, a Ree group is a group of Lie type over a finite field constructed by Ree (1960, 1961) from an exceptional automorphism of a Dynkin diagram that reverses the direction of the multiple bonds, generalizing the Suzuki groups found by Suzuki using a different method.
The C-groups include as special cases the CIT-groups, that are groups in which the centralizer of any involution is a 2-group. These were classified by Suzuki (1961, 1962), and the finite non-abelian simple ones consist of the finite non-abelian simple C-groups other than PSL 3 (2 n) and PSU 3 (2 n) for n≥2.