Thin group (finite group theory)

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

References