Abstract
We obtain the characteristic for radical algebras subgroups of whose adjoint groups are subalgebras. In particular, we prove that the algebras of this sort are nilpotent with nilpotent length at most three. We give the complete classification of those algebras under consideration which are generated by two elements.
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References
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V. O. Gorlov, “Finite nilpotent algebras with metacyclic quasiregular group,” Ukr. Mat. Zh., 47, No. 10, 1426–1431 (1995).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1646–1652, December, 1997.
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Popovich, S.V., Sysak, Y.P. Radical algebras subgroups of whose adjoint groups are subalgebras. Ukr Math J 49, 1855–1861 (1997). https://doi.org/10.1007/BF02513064
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DOI: https://doi.org/10.1007/BF02513064