An example of embedding problem with kernel of odd order is constructed so that the compatibility condition cannot be reduced to accompanying Abelian problem. Some remarks concerning examples for groups of smaller order are given. Bibliography: 7 titles
Similar content being viewed by others
References
B. N. Delone and D. K. Faddeev, “Investigations in the geometry of Galois theory,” Mat. Sb., 15(57), No. 2, 243–284 (1944).
V. V. Ishkhanov, B. B. Lur’e, and D. K. Faddeev, The Embedding Problem in Galois Theory [in Russian], Nauka, Moscow (1990).
A. V. Prokopchuk, S. V. Tikhonov, and V. I. Yanchevskii, “Generic elements in the groups SK1 for central simple algebras,” Vestsi NAN Belarusi, Ser. Fiz.-Mat. Nauk, No. 3, 35–41 (2008).
B. B. Lur’e, “Embeddability conditions when the kernel is a non-abelian p-group,” Mat. Zam., 2, No. 3, 233–238 (1967).
B. B. Lur’e, “On the concordance condition in the Galois imbedding problem,” Zap. Nauchn. Semin. POMI, 71, 155–162 (1977).
B. B. Lur’e, “The Faddeev–Hasse compatibility condition in the field embedding problem,” Zap. Nauchn. Semin. POMI, 272, 259–273 (2000).
R. Pierce, Associative Algebras [in Russian], Mir, Moscow (1986).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 443, 2016, pp. 24–32.
Rights and permissions
About this article
Cite this article
Bondarenko, M.A., Lur’e, B.B. Compatibility Condition. A Possibility of Reduction to Commutative Situation. J Math Sci 222, 380–385 (2017). https://doi.org/10.1007/s10958-017-3308-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-017-3308-5