arXiv subjects
Publications and source records attributed to F. Johari.
Let p be a prime number. We give the explicit structure of 2- nilpotent multiplier for each finite 2-generator p-group of class two. Moreover, 2-capable groups in that class are characterized.
In this paper, the structure of all finite-dimensional nilpotent Lie algebras of class two with derived subalgebra of dimension two over an arbitrary field $ \mathbb{F} $ is determined. Furthermore, we give the structure of the Schur multiplier of such Lie algebras.
We prove a theorem of splitting for the nonabelian tensor product $L \otimes N$ of a pair $(L,N)$ of Lie algebras $L$ and $N$ in terms of its diagonal ideal $L \square N$ and of the nonabelian exterior product $L \wedge N$. A similar circumstance was described two years ago by the second author in the special case $N=L$. The interest is due to the fact that the size of $L \square N$ influences strongly the structure of $L \otimes N$. Another question, often related to the structure of $L \otimes N$, deals with the behaviour of the operator $\square$ with respect to the formation of free products. We answer with another theorem of splitting even in this case, noting some connections with the homotopy theory.