On automorphism groups of some finite groups

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We show that if n>1 is odd and has no divisor p4 for any prime p, then there is no finite group G such that |Aut(G)| = n.
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[1]Gilbert, J. E., Hogan, J. A., Lakey, J. D., Atomic decomposition of divergence-free Hardy spaces, Mathematica Moraviza, 1997, Special Volume, Proc. IWAA: 33-52
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