On Schur’s theorem and its converses for n-Lie algebras

An n-Lie algebra analogue of Schur’s theorem and its converse as well as a Lie algebra analogue of Baer’s theorem and its converse are presented. Also, it is shown that, an n-Lie algebra with finite dimensional derived subalgebra and finitely generated central factor is isoclinic to some finite dimensional n-Lie algebra.     

On automorphisms of some finite <Emphasis Type="Italic">p</Emphasis>-groups

We give a sufficient condition on a finite p-group G of nilpotency class 2 so that Aut _c (G) = Inn(G), where Aut _c (G) and Inn(G) denote the group of all class preserving automorphisms and inner automorphisms of G respectively. Next we prove that if G and H are two isoclinic finite groups (in the sense of P. Hall), then Aut _c (G) ≃ Aut _c (H). Finally we study class preserving automorphisms of groups of order p ⁵, p an odd prime and prove that Aut _c (G) = Inn(G) for all the groups G of order p ⁵ except two isoclinism families.     

Some properties of isoclinism in Lie superalgebras

Abstract

Isoclinism of Lie superalgebras has been defined and studied currently. In this article, it is shown that for finite dimensional Lie superalgebras of same dimension, the notation of isoclinism and isomorphism are equivalent. Furthermore, we show that covers of finite dimensional Lie superalgebras are isomorphic using isoclinism concept.