1995
DOI: 10.4153/cjm-1995-064-3
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On 2-Groups as Galois Groups

Abstract: Let L/K be a finite Galois extension in characteristic ≠ 2, and consider a non-split Galois theoretical embedding problem over L/K with cyclic kernel of order 2. In this paper, we prove that if the Galois group of L/K is the direct product of two subgroups, the obstruction to solving the embedding problem can be expressed as the product of the obstructions to related embedding problems over the corresponding subextensions of L/K and certain quaternion algebra factors in the Brauer group of K. In connection wit… Show more

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Cited by 23 publications
(20 citation statements)
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“…4.2]. For the other two embedding problems, the obstructions in [Le1] and [Le2] are identical, although they have been rewritten slightly to accommodate the quadratic forms approach. This rewriting was done using (a, −b) = 1 (for D 8 ) and (a, −1) = 1 (for M 16 ).…”
Section: Introductionmentioning
confidence: 98%
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“…4.2]. For the other two embedding problems, the obstructions in [Le1] and [Le2] are identical, although they have been rewritten slightly to accommodate the quadratic forms approach. This rewriting was done using (a, −b) = 1 (for D 8 ) and (a, −1) = 1 (for M 16 ).…”
Section: Introductionmentioning
confidence: 98%
“…4.1] and in [Le2,2.4] are not identical, since different maps QD 8 D 4 are used. (The more natural map is the one used in [Le1], as well as in [Ki]. On the other hand, for constructing the solutions the map used in [Le2] is more convenient.)…”
Section: Introductionmentioning
confidence: 99%
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