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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.

Janko (1972) 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 Aschbacher (1976, 1978). The list of finite simple thin groups consists of:

- The projective special linear groups PSL
_{2}(*q*) and PSL_{3}(*p*) for*p*= 1 + 2^{a}3^{b}and PSL_{3}(4) - The projective special unitary groups PSU
_{3}(*p*) for*p*=−1 + 2^{a}3^{b}and*b*= 0 or 1 and PSU_{3}(2^{n}) - The Suzuki groups Sz(2
^{n}) - The Tits group
^{2}*F*_{4}(2)' - The Steinberg group
^{3}*D*_{4}(2) - The Mathieu group
*M*_{11} - The Janko group J1

- Aschbacher, Michael (1976), "Thin finite simple groups",
*Bulletin of the American Mathematical Society*,**82**(3): 484, doi:10.1090/S0002-9904-1976-14063-3, ISSN 0002-9904, MR 0396735 - Aschbacher, Michael (1978), "Thin finite simple groups",
*Journal of Algebra*,**54**(1): 50–152, doi:10.1016/0021-8693(78)90022-4, ISSN 0021-8693, MR 0511458 - Janko, Zvonimir (1972), "Nonsolvable finite groups all of whose 2-local subgroups are solvable. I",
*Journal of Algebra*,**21**: 458–517, doi:10.1016/0021-8693(72)90009-9, ISSN 0021-8693, MR 0357584