The Study Of Two Kinds Of Problems Of Schur-Ring

In this paper,we have constructed several class of finite groups such that the lattices of Schur-rings of them are special kinds of lattices.Our main results are as follows:·If the lattice of for all the Schur-rings of finite group G is a chain,then |G| ≤ 4 or |G|=p = 2m + 1,where p,m are prime.·If the lattices formed by all the Schur-rings on finite group G is a,rhombus,then |G| =4 or |G| 引 p = 2g +1,where p,q are prime.·If the lattices formed by all the Schur-rings on finite group G is a quasiantichain,then |G| =pq or p,where p,q are prime.·Let G be four-element group,we have shown that the lattices formed by all the Schur-rings on a finite group is not a modular-lattices.