Abstract
We show that a finite group G admitting an automorphism \(\alpha \) such that the function \(G\rightarrow G\), \(g\mapsto g\alpha (g)\), is bijective is necessarily solvable.
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Acknowledgements
The author would like to thank Arne Winterhof for suggesting to work on complete map**s on groups. Moreover, he would like to express his gratitude towards Peter Cameron, Michael Giudici, Laszlo Merai, Cheryl Praeger, Csaba Schneider and Arne Winterhof for some helpful comments during the work on this paper.
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Communicated by John S. Wilson.
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The author is supported by the Austrian Science Fund (FWF), project J4072-N32 “Affine maps on finite groups”.
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Bors, A. Finite groups with an automorphism that is a complete map**. Monatsh Math 193, 1–12 (2020). https://doi.org/10.1007/s00605-020-01395-7
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DOI: https://doi.org/10.1007/s00605-020-01395-7