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Arne Ledet - Some small 2-groups as Galois groups

ARNE LEDET, Department of Mathematics, Queen's University, Kingston, Ontario  K7L 3N6, Canada
Some small 2-groups as Galois groups

In 1936, Witt gave a criterion for embedding a V4-extension into a Q8-extension in terms of an equivalence of quadratic forms. Using this result, it is possible to give similar criteria for solving other embedding problems, starting with embedding a D4-extension into a QD8-extension, where D4 and QD8 are the dihedral and quasi-dihedral groups of order 8 and 16, resp. This again permits a complete description of extensions with certain 2-groups of order 16 as Galois groups.