- See also
- References
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. {{harvtxt|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 {{harvs|txt|last=Aschbacher|year1=1976|year2=1978}}. The list of finite simple thin groups consists of: - The projective special linear groups PSL2(q) and PSL3(p) for p = 1 + 2a3b and PSL3(4)
- The projective special unitary groups PSU3(p) for p =−1 + 2a3b and b = 0 or 1 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 alsoReferences- {{Citation | last1=Aschbacher | first1=Michael | author1-link=Michael Aschbacher | title=Thin finite simple groups | url=http://www.ams.org/journals/bull/1976-82-03/S0002-9904-1976-14063-3/home.html | doi=10.1090/S0002-9904-1976-14063-3 | mr=0396735 | year=1976 | journal=Bulletin of the American Mathematical Society | issn=0002-9904 | volume=82 | issue=3 | pages=484}}
- {{Citation | last1=Aschbacher | first1=Michael | author1-link=Michael Aschbacher | title=Thin finite simple groups | doi=10.1016/0021-8693(78)90022-4 | mr=511458 | year=1978 | journal=Journal of Algebra | issn=0021-8693 | volume=54 | issue=1 | pages=50–152}}
- {{Citation | last1=Janko | first1=Zvonimir | title=Nonsolvable finite groups all of whose 2-local subgroups are solvable. I | doi=10.1016/0021-8693(72)90009-9 | mr=0357584 | year=1972 | journal=Journal of Algebra | issn=0021-8693 | volume=21 | pages=458–517}}
1 : Finite groups |