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Maximal $/textrm {PSL}_2$ Subgroups of Exceptional Groups of Lie Type (Paperback)
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Maximal $/textrm {PSL}_2$ Subgroups of Exceptional Groups of Lie Type (Paperback)
Series: Memoirs of the American Mathematical Society
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We study embeddings of PSL2(pa) into exceptional groups G(pb)forG =
F4,E6,2E6,E7,andp aprimewitha,b positive integers. With a few
possible exceptions, we prove that any almost simple group with
socle PSL2(pa), that is maximal inside an almost simple exceptional
group of Lie type F4, E6, 2E6 and E7, is the fixed points under the
Frobenius map of a corresponding maximal closed subgroup of type A1
inside the algebraic group. Together with a recent result of
Burness and Testerman for p the Coxeter number plus one, this
proves that all maximal subgroups with socle PSL2(pa) inside these
finite almost simple groups are known, with three possible
exceptions (pa = 7, 8,25 for E7). In the three remaining cases we
provide considerable information about a potential maximal
subgroup.
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