Finite Group Theory: Index

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Derangements in simple and primitive groups (2002, methodology): “raic group and only the ﬁeld size is varying. We can use methods of algebraic geometry and algebraic groups to study this situation. We recall that F∗(H) is the generalized Fitting subgroup of H. See [A1]. In particular, F∗(H) simple just means that F∗(H) ≤ H ≤ Aut(H). There is no harm in considerin”
The rational function analogue of a question of Schur and exceptionality of permutation representations (2002, unknown): “and so J/Z(F∗(J)) embeds in Aut(F∗(J))). We say Jis almost simple if F∗(J) is a nonabelian simple subgroup. Note that this is equivalent to L⊆ J ⊆ Aut(L) for Lnonabelian simple (and so L= F∗(J)). See [Asc86], [Hup67], or [Suz82] for more details on these concepts. We use the Aschbacher–O’Nan–Scott c”
A Machine-Checked Proof of the Odd Order Theorem (2013, methodology): “For more advanced material we have used Aschbacher’s and Gorenstein’s books [3, 22] and some sources adapted to Galois theory and commutative algebra [30, 33, 37].”