In virtue of a recent bound obtained in [P. Niroomand and F.G. Russo, A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra 39 (2011), 1293--1297], we classify all capable nilpotent Lie algebras of finite dimension possessing a derived subalgebra of dimension one. Indirectly, we find also a criterion for detecting noncapable Lie algebras. The final part contains a construction, which shows that there exist capable Lie algebras of arbitrary big corank (in the sense of Berkovich--Zhou)

The purpose of this paper is a further investigation on the 2-nilpotent multiplier, M(2) (G), when G is a non-abelian p-group. Furthermore, taking G in the class of extra-special p-groups, we will get the explicit structure of M(2) (G) and will classify 2-capable groups in that class.2010 Mathematics Subject Classification. 20C25, 20D15.

No abstract

In this paper, we present an explicit structure for the Baer invariant of a free nilpotent group ( the n-th nilpotent product of the infinite cyclic group, Z n * Z n * . . . n * Z) with respect to the variety of polynilpotent groups of class row (c, 1), N c,1 , for all c > 2n − 2. In particular, an explicit structure of the Baer invariant of a free abelian group with respect to the variety of metabelian groups will be presented.