A chain condition for groups
Thomas S. Shores · Rocky Mountain Journal of Mathematics · 1973
In this article a chain condition for groups, called the bounded chain condition, is studied; this chain condition includes the ascending and descending chain conditions as special cases.It is shown that every locally radical group which satisfies the bounded chain condition on subgroups must satisfy the ascending or descending chain condition on subgroups, i.e., such groups are Artinian or Noetherian.The same conclusion holds for nilpotent groups which satisfy the bounded chain condition on abelian subgroups.