We reduce the graph isomorphism problem to 2-nilpotent p-groups isomorphism problem (and to finite 2-nilpotent Lie algebras the ring Z/pZ. Furthermore, we show that classifying problems in categories graphs, finite 2-nilpotent p-groups, and 2-nilpotent Lie algebras over Z/pZ are polynomially equivalent and wild.

In the first part, we prove that the dominion (in the sense of Isbell) of a subgroup of a finitely generated nilpotent group is trivial in the category of all nilpotent groups. In the second part, we show that the dominion of a subgroup of a finitely generated nilpotent group of class two is trivial in the category of all metabelian nilpotent groups. Section

In a recent article [Gi99], V.Ginzburg introduced and studied in depth the notion of a principal nilpotent pair in a semisimple Lie algebra g. He also obtained several results for more general pairs. As a next step, we considered in [Pa99] almost principal nilpotent pairs. The aim of this paper is to make a contribution to the general theory of nilpotent pairs. Roughly speaking, a nilpotent pai...

If I is a (two-sided) ideal of ring R, we let $${\text {ann}}_l(I)=\{r\in R\mid rI=0\},$$ {ann}}_r(I)=\{r\in Ir=0\},$$ and {ann}}(I)={\text {ann}}_l(I)\cap {\text {ann}}_r(I)$$ be the left, right double annihilators. An said to an annihilator if $$I={\text {ann}}(J)$$ for some J (equivalently, {ann}}({\text {ann}}(I))=I$$ ). We study ideals Leavitt path algebras graph $$C^*$$ -algebras. Let $$L...

We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. In particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplicati...

‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of ...