On a Class of Lattice Semigroup Functors

In the paper, continuum many natural transitive lattice subgroup functors corresponding to no hereditary lattice formation are constructed on the class of all finite groups. This result is an answer to Question 15.39 in “The Kourovka Notebook”, which was posed by the author and A. F. Vasilev in connection with their theorem claiming that, on the class of all solvable groups, all functors of this kind correspond to hereditary local lattice formations.