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This extension contains an algebraic extension
:<math>F = \mathbf {Q}\left(\sqrt{(-1)^\frac{p-1}{2}p}\right)</math>
of '''Q'''. If we extend the field of constants to be ''F'', we now have an extension with Galois group PSL<sub>2</sub>(p), the [[projective linear group|projective special linear group]] of the field with p elements, which is a finite simple group. By specializing y to a specific field element, we can, outside of a thin set, obtain an infinity of examples of fields with Galois group PSL<sub>2</sub>(p) over ''F'', and PGL<sub>2</sub>(p) over '''Q'''.
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