P-normal-extensible automorphism

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Suppose p is a prime number and P is a p-group (i.e., a group where the order of every element is a power of p). An automorphism \sigma of P is termed a p-normal-extensible automorphism if, for any p-group Q containing P as a normal subgroup, there exists an automorphism \sigma' of Q whose restriction to P equals \sigma.