ON THE CLASSIFICATION OF PSL (2,Pn)

We say that a finite group G is a DN-group if for each subgroup H of G,H' ≤G and we say that a finite group G is a minimal non-DN-group if G is not DN-group but each proper subgroup of G is a DN-group. In this paper we prove that if G is a simple minimal non-DN-group then G is isomorphic to PSL(2,pn), for appropriate p,n. By this, we obtain a classification of nonsolvable minimal non-DN-groups.

Keywords:

normal subgroup , derived subgroup , solvable groups , simple group