47 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