Abstract
For a finite group G and a field k,we call a G-Galois extension over k by G/k-extension. Whether a G/k-extension exists or not is the first version of inverse Galois problem. Especially the case when k = Q the rational number field, plays an important role in the study of the absolute Galois Group of Q. By many mathematicians, the existence of G/Q-extensions has been shown for a lot of finite groups G by now (cf. Malle-Matzat [14], Serre [19], etc.)
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Rikuna, Y. (2004). Explicit Constructions of Generic Polynomials for Some Elementary Groups. In: Hashimoto, Ki., Miyake, K., Nakamura, H. (eds) Galois Theory and Modular Forms. Developments in Mathematics, vol 11. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0249-0_9
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