651 research outputs found
Non abelian tensor square of non abelian prime power groups
For every -group of order with the derived subgroup of order ,
Rocco in \cite{roc} has shown that the order of tensor square of is at most
. In the present paper not only we improve his bound for
non-abelian -groups but also we describe the structure of all non-abelian
-groups when the bound is attained for a special case. Moreover, our results
give as well an upper bound for the order of .Comment: enriched with contributions of F.G. Russ
Structure of nilpotent Lie algebra by its multiplier
For a finite dimensional Lie algebra , it is known that
s(L)=\f{1}{2}(n-1)(n-2)+1-\mathrm{dim} M(L) is non negative. Moreover, the
structure of all finite nilpotent Lie algebras is characterized when
in \cite{ni,ni4}. In this paper, we intend to characterize all nilpotent Lie
algebra while $s(L)=2.
Characterization of finite dimensional nilpotent Lie algebras by the dimension of their Schur multipliers,
It is known that the dimension of the Schur multiplier of a non-abelian
nilpotent Lie algebra of dimension is equal to
for some . The structure of all
nilpotent Lie algebras has been given for in several papers.
Here, we are going to give the structure of all non-abelian nilpotent Lie
algebras for
Capability of Nilpotent Lie algebras with small derived Subalgebra
In this paper, we classify all capable nilpotent Lie algebras with derived
subalgebra of dimension at most 1.Comment: To appear in J. Algebra with new contributions of F.G. Russ
- …