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Imbedding problem with non-Abelian kernel of order p4

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This paper considers the imbedding problem for numerical fields and p-groups with nonabelian kernel of order p4, two generators α and β, and defining relations\(\alpha ^{p^2 } \)=1, βp=1, [α,β,α]=1, and [α,β,β]= 1. For p=2 and “almost always” for odd p, the Hasse principle is valid,” and the problem is solvable if and only if all related local problems are solvable. Counterexamples in which the Hasse principle is not valid are constructed for some exceptional cases.

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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 175, pp. 46–62, 1989.

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Ishkhanov, V.V., Lur'e, B.B. Imbedding problem with non-Abelian kernel of order p4 . J Math Sci 57, 3473–3481 (1991). https://doi.org/10.1007/BF01100115

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  • Local Problem
  • Exceptional Case
  • Numerical Field
  • Hasse Principle