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Article

Safonova, L. V. ; Shchukin, K. K.
On centrally nilpotent loops. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 41 (2000), issue 2, pp. 401-404
MSC: 20B35, 20N05, 22A30, 53A60, 53C05, 53C22, 53C35 | MR 1780880 | Zbl 1038.20052
Keywords:
group; subnormal subgroup; loop; multiplication group; inner permutation group
Summary:
Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.
References:
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[2] Safonova L.V., Shchukin K.K.: About n-Engel elements of groups. 12-th Algebr. Coll. of USSR, Thesis-book 1 Sverdlovsk (1973), 54.
[3] Smith J.D.: Multiplication groups of quasigroups. Preprint 603, Technische Hochschule Darmstadt (1981).
[4] Bruck R.H.: A Survey of Binary Systems. Springer-Verlag (1966). MR 0093552 | Zbl 0141.01401
[5] Shchukin K.K.: On nilpotency of the multiplication group of an $A$-loop. Mat. Issled. 162 (1988), 116-117. MR 0947466 | Zbl 0664.20043
[6] Macdonald D., Neumann B.H.: A third-Engel 5-group. J. Austral. Math. Soc. 7 (1967), 555-569. MR 0222171 | Zbl 0163.02502
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