A Simple Proof of Baer's and Sato's Theorems on Lattice Isomorphisms between Groups

A group $G$ is said to be an $M\sp*$-group if all subgroups of $G$ are quasinormal and $G$ is quaternionfree. Using Iwasawa's characterization of $M\sp*$-groups the author gives an elegant and unified proof of the following theorem: If $G$ is an $M\sp*$-group, then there exists an abelian group $A$ such that the lattices of subgroups of $A$ and $G$ are isomorphic. [J.Chvalina (Brno)]