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On the order of the Sylow subgroups of the automorphism group of a finite group

Published online by Cambridge University Press:  18 May 2009

K. H. Hyde
K. H. Hyde
Affiliation:
Weber State College, Ogden, Utah, U.S.A.
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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.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 11 , Issue 2 , July 1970 , pp. 88 - 96
Copyright
Copyright © Glasgow Mathematical Journal Trust 1970

References

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