Geodesic
On the order of the Sylow subgroups of the automorphism group of a finite group
Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 88-96

Voir la notice de l'article provenant de la source Cambridge University Press

Given any finite group G, we wish to determine a relationship between the highest power of a prime p dividing the order of G, denoted by |G|p, and |A(G)|p, where A(G) is the automorphism group of G. It was shown by Herstein and Adney [8] that |A(G)|p ≧ p whenever |G|p= ≧P2. Later Scott [16] showed that A(G)p≧P2. For the special case where G is abelian, Hilton [9] proved that Adney [1] showed that this result holds if a Sylow p-subgroup of G is abelian, and gave an example where |G|p= p4 and |A(G)|P =p2. We are able to show in Theorem 4.5 that, if |G|p = ≧ p5, then |A(G)| = ≧ p3. 
Hyde, K. H. On the order of the Sylow subgroups of the automorphism group of a finite group. Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 88-96. doi: 10.1017/S0017089500000902
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