The aim of this paper is to show a close relationship between the factoralgebras by the terms of the upper central series ζ n (L) of a Leibniz algebra L and the terms of its lower central series γ n (L). Specifically we show that finiteness of codimension of some ζ k (L) implies finiteness of dimension of γ k+1 (L) and give explicit bounds for this dimension. We also improve this in the case k = 1, which corresponds to the center and commutator subalgebra of the algebra, respectively. These results are analogous to the results that have been obtained for groups and Lie algebras.

In this paper we obtain the description of the Leibniz algebras whose subalgebras are ideals.

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The aim of this paper is to describe some “minimal” Leibniz algebras, that are the Leibniz algebras whose proper subalgebras are Lie algebras, and the Leibniz algebras whose proper subalgebras are abelian.

Dedicated to to the memory of D. I. Zaicev on the 60th anniversary of his birth. AbstractA group G is called a group with boundedly finite conjugacy classes (or a BFC-group) if G is finite-by-abelian. A group G satisfies the maximal condition on non-BFC-subgroups if every ascending chain of non-BFC-subgroups terminates in finitely many steps. In this paper the authors obtain the structure of finitely generated soluble-by-finite groups with the maximal condition on non-BFC subgroups.