a group $g$ is called metahamiltonian if all its non-abelian subgroups are normal‎. ‎the aim of this paper is to provide an updated survey of research concerning certain classes of generalized metahamiltonian groups‎, ‎in various contexts‎, ‎and to prove some new results‎. ‎some open problems are listed‎.

An algebraic construction for constant dimension subspace codes is called orbit code. It arises as the orbits under the action of a subgroup of the general linear group on subspaces in an ambient space. In particular orbit codes of a Singer subgroup of the general linear group has investigated recently. In this paper, we consider the normalizer of a Singer subgroup of the general linear group a...

Let X be a non-degenerate left Banach module over a normed algebra A having a bounded approximate left identity. We show that, if A is a left ideal of a larger algebra, then this representation can be extended to a representation of the larger algebra. Based on this result, we study in detail the existence and properties of representations of the various centralizer algebras of A which are comp...

groups of infinite rank in which every subgroup is either normal or self-normalizing are characterized in terms of their subgroups of infinite rank.

a subgroup $x$ of a group $g$ is almost normal if the index $|g:n_g(x)|$ is finite, while $x$ is nearly normal if it has finite index in the normal closure $x^g$. this paper investigates the structure of groups in which every (infinite) subgroup is either almost normal or nearly normal.

Abstract We study toric G -solid Fano threefolds that have at most terminal singularities, where is an algebraic subgroup of the normalizer a maximal torus in their automorphism groups. All varieties are assumed to be projective and defined over field complex numbers.

We study orbit codes in the field extension $ \mathbb{F}_{q^n} $. First we show that automorphism group of a cyclic code is contained normalizer Singer subgroup if generated by subspace not proper subfield then generalize to orbits under subgroup. In situation some exceptional cases arise and open remain. Finally characterize linear isometries between such codes.