Abstract
It is shown that any neutral polyverbal subgroup W is generated as a subgroup by the set of its fully neutral polywords, and a necessary and sufficient condition is given for an associative neutral polyverbal operation to be verbal. The associativity of verbal operations follows easily from these results and O. N. Golovin's theorem.
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O. N. Golovin, “Polyidentical correlations in groups,” Tr. Matem. Ob-va,12, 413–435 (1968).
S. Moran, “Associative operations on groups. I,” Proceedings of the London Mathematical Society,6, No. 24, 581–596 (1956).
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S. A. Ashmanov and O. N. Matsedonskaya, “Regular operations satisfying Mal'tsev's postulate,” Sibirsk. Matem. Zh.,7, No. 6, 1216–1229 (1966).
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Translated from Matematicheskie Zametki, Vol. 4, No. 1, pp. 85–89, July, 1968.
The author thanks O. N. Golovin for his assistance.
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Matsedonskaya, O.N. Neutral polyverbal operations. Mathematical Notes of the Academy of Sciences of the USSR 4, 540–542 (1968). https://doi.org/10.1007/BF01429817
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DOI: https://doi.org/10.1007/BF01429817