Classical involution theorem

In mathematical finite group theory, the classical involution theorem of Aschbacher ( 1977a , 1977b , 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. Berkman (2001) extended the classical involution theorem to groups of finite Morley rank.

A classical involutiont of a finite group G is an involution whose centralizer has a subnormal subgroup containing t with quaternion Sylow 2-subgroups.

References

• Aschbacher, Michael (1977a), "A characterization of Chevalley groups over fields of odd order", Annals of Mathematics , Second Series, 106 (2): 353–398, doi:10.2307/1971100, ISSN   0003-486X, JSTOR   1971100, MR   0498828
• Aschbacher, Michael (1977b), "A characterization of Chevalley groups over fields of odd order II", Annals of Mathematics , Second Series, 106 (3): 399–468, doi:10.2307/1971063, ISSN   0003-486X, JSTOR   1971063, MR   0498829
• Aschbacher, Michael (1980), "Correction to: A characterization of Chevalley groups over fields of odd order. I, II", Annals of Mathematics , Second Series, 111 (2): 411–414, doi:10.2307/1971101, ISSN   0003-486X, MR   0569077
• Berkman, Ayşe (2001), "The classical involution theorem for groups of finite Morley rank", Journal of Algebra , 243 (2): 361–384, doi: 10.1006/jabr.2001.8854 , hdl: 11511/64007 , ISSN   0021-8693, MR   1850637