Geodesic
Finite groups with small automizers of their nonabelian subgroups
Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 59-64

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Let G be a group and let H be a subgroup of G. The automizer AutG(H) of H in G is defined as the group of automorphisms of H induced by conjugation of elements of NG(H). Thus AutG(H)≅NG(H)/CG(H), and we obviously have $$\tfrm{In(}H\tfrm{)≤Aut}_{G}\tfrm{(}H\tfrm{)≤Aut(}H\tfrm{).}$$ We call AutG(H) large if AutG(H)=Aut(H) and small if AutG(H)=In(H). 
BRANDL, ROLF; DEACONESCU, MARIAN. Finite groups with small automizers of their nonabelian subgroups. Glasgow mathematical journal, Tome 41 (1999) no. 1, pp. 59-64. doi: 10.1017/S0017089599970325
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