The object of this paper is to find a necessary and sufficient condition for a pair of groups G1 and G2 so that every normal subgroup of G1×G2 is of the type N1×N2 where Ni E Gi, i = 1, 2

Let G be a reductive algebraic group, P a parabolic subgroup of G with unipotent radical Pu, and A a closed connected unipotent subgroup of Pu which is normalized by P. We show that P acts on A with nitely many orbits provided A is abelian. This generalizes a well-known niteness result, namely the case when A is central in Pu. We also obtain an analogous result for the adjoint action of P on in...

1. INTRODUCTION. In this article we show that group representations permit simple, visual explanations of semidirect products and related concepts. Along the way, we prove an extension of Cayley's theorem, define blocks and tails for the resulting representations, and investigate the title question: Do normal subgroups have straight tails? We consider representations of finite groups over the f...

Many studies have investigated the lattice structure of fuzzy substructures of algebraic sets such as group and ring. Some important results about modularity and distributivity have been obtained in these studies. In this paper, we first define the notion of (normal) (λ,μ)-L-subgroups on a group and investigate some of their properties. In particular, we discuss the relationships among ordinary...