On The Orders of Automorphism Groups of Finite Groups |
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| Authors: | Bray John N; Wilson Robert A |
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| Institution: | School of Mathematical Sciences, Queen Mary, University of London Mile End Road, London E1 4NS, United Kingdom; J.N.Bray{at}qmul.ac.uk, R.A.Wilson{at}qmul.ac.uk |
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| Abstract: | In the Kourovka notebook, Deaconescu asks whether |AutG|  (|G|)for all finite groups G, where denotes the Euler totient function,and whether G is cyclic whenever |AutG|. Both questions areanswered in the negative in this paper. Moreover, |AutG|/(|G|)can be made arbitrarily small. 2000 Mathematics Subject Classification20E36 (primary), 20F28 (secondary). |
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