I am looking for all finite groups $G$ such that for each subgroup $H$ of $G$ and each automorphism $\sigma$ of $H$ there exists an automorphism $\psi$ of $G$ whose restriction to $H$ is $\sigma$. Is there any reference on this problem?



Groups with special automorphism group
These groups are called the groups of *injective type*.
It is known that nonabelian finite groups of injective type have even order.


See the following papers:   

<http://dx.doi.org/10.1017/S0017089512000031>
  

<http://dx.doi.org/10.1142/S0219498807002235>


