L. A. Shemetkov posed a Problem 9.74 in Kourovka Notebook to find all local formations \({\mathfrak {F}}\) of finite groups such that every finite minimal non- \({\mathfrak {F}}\) -group is either a Schmidt group or a group of prime order. All known solutions to this problem are obtained under the assumption that every minimal non- \({\mathfrak {F}}\) -group is soluble or under the equivalent one. Using the above mentioned solutions we present a polynomial in n time check for a local formation \({\mathfrak {F}}\) with bounded \(\pi ({\mathfrak {F}})\) to be a formation of soluble groups with the Shemtkov property where \(n=\max \pi ({\mathfrak {F}})\) .
