in this paper, we consider locally graded groups in which every non-permutable subgroup is soluble of bounded derived length.

it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...

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

We obtain a complete structural characterization of Cohn-Leavitt algebras over no-exit objects as graded involutive algebras. Corollaries of this result include graph-theoretic conditions characterizing when a Leavitt path algebra is a directed union of (graded) matricial algebras over the underlying field and over the algebra of Laurent polynomials and when the monoid of isomorphism classes of...

We show that every graded locally finite right noetherian algebra has sub-exponential growth. As a consequence, every noetherian algebra with exponential growth has no finite dimensional filtration which leads to a right (or left) noetherian associated graded algebra. We also prove that every connected graded right noetherian algebra with finite global dimension has finite GK-dimension. Using t...