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# 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 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, 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, ISSN 0003-486X, JSTOR 1971063, MR 0498828

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 569077

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, ISSN 0021-8693, MR 1850637

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