// Workers AI · dad joke modeWhat did the classical involution theorem say to its friend? "Let's invert our relationship.

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 involution t 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