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On Two Problems Concerning Neutral Polyverbal Operations on Groups

Published online by Cambridge University Press:  20 November 2018

O. N. Macedonska-Nosalska
O. N. Macedonska-Nosalska*
Affiliation:
Institute of Mathematics, GliwicePoland York University, Toronto
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In his paper [2] O. N. Golovin introduced the notion of a neutral polyverbal operation on groups, of which Moran's verbal operations [4] and Gruenberg's and Šmelkin's operations [3,5] are special cases. The free and direct multiplication we shall call here trivial operations. It is known [5,4] that Mal'cev's postulate does not hold for nontrivial verbal operations but the postulate of associativity does.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 18 , Issue 5 , 01 December 1975 , pp. 763 - 765
Copyright
Copyright © Canadian Mathematical Society 1975

References

1. Ašmanov, C.A., Macedonskaya, O.N., On regular operations satisfying MaPcev's postulate. Sib. Matem. Žurnal VII, N6, 1216-1229, (1966).Google Scholar
2. Golovin, O.N., Poly-identical relations in groups, Tr. Mosk. Matem. Ob-va, 12, 413-435 (1963).Google Scholar
3. Gruenberg, K., Residual properties of infinite soluble groups, Proc. London. Math. Soc, 7, No. 25, 29-62 (1957).Google Scholar
4. Moran, S., Associative operations on groups, L, Proc. Lond. Math. Soc, 6, No. 24, 581-596 (1956).Google Scholar
5. Šmel’kin, A.L., On the theory of regular products of groups. Matem. Sbornik, 51, No. 2, 277-292 (1960).Google Scholar