In this chapter we complete the proof of Cherlin’s conjecture by handling the classical groups. Our main result shows that, if G is an almost simple primitive group on a set Ω having socle a simple classical group, then either G is not binary or |Ω|∈{5, 6, 8}. The proof uses some of the results in the first two chapters together with detailed information on the maximal subgroups of G.
Gill, N., Liebeck, M., Spiga, P. (2022). Classical Groups. In N. Gill, M.W. Liebeck, P. Spiga (a cura di), Cherlin’s Conjecture for Finite Primitive Binary Permutation Groups (pp. 103-207). Springer Science and Business Media Deutschland GmbH [10.1007/978-3-030-95956-2_4].
Classical Groups
Spiga P.
2022
Abstract
In this chapter we complete the proof of Cherlin’s conjecture by handling the classical groups. Our main result shows that, if G is an almost simple primitive group on a set Ω having socle a simple classical group, then either G is not binary or |Ω|∈{5, 6, 8}. The proof uses some of the results in the first two chapters together with detailed information on the maximal subgroups of G.
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Gill-2022-Lect Notes Math-preprint.pdf
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