summary:[For the entire collection see Zbl 0742.00067.]\par Let {\germ g}\sb k be the Lie algebra {\germ gl}(k,\mathcal{C}), and let U\sb k be the universal enveloping algebra for {\germ g}\sb k. Let Z\sb k be the center of U\sb k. The authors consider the chain of Lie algebras {\germ g}\sb n\supset {\germ g}\sb{n-1}\supset\dots\supset {\germ g}\sb 1. Then Z=\langle Z\sb k\mid k=1,2,\dots n\rangle is an associative algebra which is called the Gel'fand-Zetlin subalgebra of U\sb n. A {\germ g}\sb n module V is called a GZ-module if V=\sum\sb x\oplus V(x), where the summation is over the space of characters of Z and V(x)=\{v\in V\mid(a-x(a))\sp mv=0, m\in\mathcal{Z}\sb +, a∈Z}. The authors describe several properties of GZ- modules. For example, they prove that if V(x)=0 for some x and the module V is simple, then V is a GZ-module. Indecomposable GZ- modules are also described. The authors give three conjectures on GZ- modules and
