As the title says,I want to know the maximal subgroup of the group whose socle is $Sz(q)$. If there are such papers,could you tell its name or give me a link. Thank a lot
2026-02-23 07:45:18.1771832718
If a group 's socle is $Sz(q)$, how can I determine its maximal subgroup
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Suzuki's original paper on the Suzuki groups is:
M. Suzuki. On a class of doubly transitive groups. Ann. of Math. (2) 75 (1962), 105–145.
He classifies the maximal subgroup of the groups themselves, but not of their almost simple extensions.
It turns out that there are o novelty subgroups in the almost simple extensions, so their maximals are just the normalizers of the maximals of the Suzuki group together with those containing the socle. This is proved in Chapter 7 of the recently published book:
The Maximal Subgroups of the Low-Dimensional Finite Classical Groups J.N. Bray, D.F. Holt, C.M. Roney-Dougal, London Mathematical Society Lecture Note Series 407, CUP, 2013.
http://www.cambridge.org/co/academic/subjects/mathematics/algebra/maximal-subgroups-low-dimensional-finite-classical-groups