author={D. Roberts},
  journal={International Journal of Number Theory},
  • D. Roberts
  • Published 2011
  • Mathematics
  • International Journal of Number Theory
We present the first explicitly known polynomials in Z(x) with nonsolvable Galois group and field discriminant of the form ±p A for p 7 a prime. Our main polyno- mial has degree 25, Galois group of the form PSL2(5) 5 .10, and field discriminant 5 69 . A closely related polynomial has degree 120, Galois group of the form SL2(5) 5 .20, and field discriminant 5 311 . We completely describe 5-adic behavior, finding in particular that the root discriminant of both splitting fields is 125·5 1/12500… Expand

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