{{Short description|Mathematical finite group theory}} In mathematical finite group theory, the '''classical involution theorem''' of {{harvs|txt|last=Aschbacher|year1=1977a|year2=1977b|year3=1980}} classifies simple groups with a classical involution and satisfying some other conditions, showing that they are mostly groups of Lie type over a field of odd characteristic. {{harvtxt|Berkman|2001}} extended the classical involution theorem to groups of finite Morley rank.
A '''classical involution''' ''t'' of a finite group ''G'' is an involution whose centralizer has a subnormal subgroup containing ''t'' with quaternion Sylow 2-subgroups.
==References== *{{Citation | last1=Aschbacher | first1=Michael | author1-link=Michael Aschbacher | title=A characterization of Chevalley groups over fields of odd order | jstor=1971100 | mr=0498828 | year=1977a | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=106 | issue=2 | pages=353–398 | doi = 10.2307/1971100 }} *{{Citation | last1=Aschbacher | first1=Michael | author1-link=Michael Aschbacher | title=A characterization of Chevalley groups over fields of odd order II | jstor=1971063 | mr=0498829 | year=1977b | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=106 | issue=3 | pages=399–468 | doi = 10.2307/1971063 }} *{{Citation | last1=Aschbacher | first1=Michael | author1-link=Michael Aschbacher | title=Correction to: A characterization of Chevalley groups over fields of odd order. I, II | doi=10.2307/1971101 | mr=569077 | year=1980 | journal=Annals of Mathematics |series=Second Series | issn=0003-486X | volume=111 | issue=2 | pages=411–414}} *{{Citation | last1=Berkman | first1=Ayşe | title=The classical involution theorem for groups of finite Morley rank | doi=10.1006/jabr.2001.8854 | mr=1850637 | year=2001 | journal=Journal of Algebra | issn=0021-8693 | volume=243 | issue=2 | pages=361–384| doi-access=free | hdl=11511/64007 | hdl-access=free }}
Category:Theorems about finite groups
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