The inverse Galois problem is a major question in mathematics. For a given base field and a given finite group G, one would like to list all Galois extensions L/F such that the Galois group of L/F is G.

In this work we shall solve this problem for all fields F , and for group G of unipotent 4 × 4 matrices over F_2 . We also list all 16 U_4 (F_2 )- extensions of Q_2 . The importance of these results is that they answer the inverse Galois problem in some specific cases. This is joint work with Jan Minac and Nguyen Duy Tan.

Organizational Meeting of the Western NCG group.