Title: Finite groups with small automizers of their nonabelian subgroups
Abstract: Let G be a group and let H be a subgroup of G . The automizer Aut G ( H ) of H in G is defined as the group of automorphisms of H induced by conjugation of elements of N G ( H ). Thus Aut G ( H )≅ N G ( H )/ C G ( H ), and we obviously have $$\tfrm{In(}H\tfrm{)≤Aut}_{G}\tfrm{(}H\tfrm{)≤Aut(}H\tfrm{).}$$ We call Aut G ( H ) large if Aut G ( H )=Aut( H ) and small if Aut G ( H )=In( H ).