Abstract
We select canonical decompositions of the isotopes of groups, show that they are unique, and establish relationships between them. We also obtain external characteristics of the identities which imply the linearity or alinearity of the isotopy and the commutativity of the corresponding group. We describe the identities of linear isotopes of Abelian groups, i.e., ofT-quasigroups, and suggest a new method for the description of isotopic closures of classes of groups.
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Reference
F. N. Sokhatskii, “On isotopes of groups. I,”Ukr. Mat. Zh.,47, No. 10, 1387–1398 (1995).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 12, pp. 1692–1703, December, 1995.
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Sokhatskii, F.N. On isotopes of groups. II. Ukr Math J 47, 1935–1948 (1995). https://doi.org/10.1007/BF01060967
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DOI: https://doi.org/10.1007/BF01060967