Products of groups and local nearrings

Abstract

Groups which can be written as a product $G=AB$ of two of its subgroups $A$ and $B$ have been studied by many authors. A particular role in such investigations play groups of the form $G=AB=AM=BM$ where $M$ is a normal subgroup of $G$ and $A\cap M=B\cap M=1$. It turns out that there is a close connection between groups of this form and some nearrings, especially so called local nearrings, so that many problems concerning such nearrings can be reduced to questions about these groups. In the following we will discuss different aspects of this connection and, in addition, consider in detail certain structural questions arised in the case of almost cyclic subgroups $A$ an $B$.