In the mathematical classification of finite simple groups, a thin group is a finite group such that for every odd prime number p, the Sylow p-subgroups of the 2-local subgroups are cyclic. Informally, these are the groups that resemble rank 1 groups of Lie type over a finite field of characteristic 2.
defined thin groups and classified those of characteristic 2 type in which all 2-local subgroups are solvable. The thin simple groups were classified by . The list of finite simple thin groups consists of: The projective special linear groups PSL2(q) The projective special linear groups PSL3(p) for p = 1 + 2a or p = 1 + 2a3, and PSL3(4) The projective special unitary groups PSU3(p) for p = 1 - 2a or p = 1 - 2a3, and PSU3(2n) The Suzuki groups Sz(2n) The Tits group 2F4(2)' The Steinberg group 3D4(2) The Mathieu group M11 The Janko group J1
See also Quasithin group
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