In the theory of algebraic groups, a special group is a linear algebraic group G with the property that every principal G-bundle is locally trivial in the Zariski topology.
Special groups are necessarily connected.
The projective linear group is not special because there exist Azumaya algebras, which are trivial over a finite separable extension, but not over the base field.
Special groups were defined in 1958 by Jean-Pierre Serre[1] and classified soon thereafter by Alexander Grothendieck.
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