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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 outer automorphism group is cyclic of order 2n+1, given by automorphisms of the field ...
In the mathematical discipline known as group theory, the phrase Suzuki group refers to: 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
In the area of modern algebra known as group theory, the Suzuki group Suz or Sz is a sporadic simple group of order 448,345,497,600 = 2 13 · 3 7 · 5 2 · 7 · 11 · 13 ≈ 4 × 10 11 . History
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 simple groups whose order is not divisible by 3. They are not related to the sporadic Suzuki group.
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. He classified several classes of simple groups of small rank, including the CIT-groups and C-groups and CA-groups. There is also a sporadic simple group called the Suzuki group, which he
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 similar construction gives the Hall–Janko group J 2 (order 604,800) as the quotient of the group of quaternionic automorphisms of Λ by the group ±1 of scalars. The seven simple groups described above comprise what Robert Griess calls the second generation of the Happy Family , which consists of the 20 sporadic simple groups found within ...
Isoclinism is used in theory of projective representations of finite groups, as all Schur covering groups of a group are isoclinic, a fact already hinted at by Hall according to Suzuki (1982, p. 256). This is used in describing the character tables of the finite simple groups (Conway et al. 1985, p. xxiii, Ch. 6.7).