Explicit infinite families of PSL(n,q) and PSU(n,q) are realized as Galois groups over Q with unbounded degree and proper containment inside PGL/PGU.
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Simple Lie Groups of type An as Galois groups over Q
Explicit infinite families of PSL(n,q) and PSU(n,q) are realized as Galois groups over Q with unbounded degree and proper containment inside PGL/PGU.