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Characterization of groups of involutions by means of composite functional equations in two variables

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Abstract

The groups all of whose elements are involutions are characterized by means of two equivalent composite functional equations in two variables.

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References

  1. J. Aczél and J. Dhombres, Functional Equations in Several Variables, Encyclopedia of Mathematics and its Applications, vol. 31, Cambridge University Press (Cambridge, 1989).

  2. R. P. Agarwal, J. Brzdęk, and J. Chudziak, Stability problem for the composite type functional equations, Expo. Math., 36 (2018), 178–196.

  3. P. Burai, A. Házy, and T. Juhász, A composite functional equation from algebraic aspect, Aequationes Math., 86 (2013), 57–64.

  4. J. G. Dhombres, Solution générale sur un groupe abélien de l’équation fonctionnelle f(xf(y)) = f(f(x) ∗ y), Aequationes Math., 15 (1977), 173–193.

  5. P. Kahlig, A. Matkowska, and J. Matkowski, On a class of composite functional equations in a single variable, Aequationes Math., 52 (1996), 260–283.

  6. A. J. Malcolm, The involution width of finite simple groups, J. Algebra, 493 (2018), 297–340.

  7. J. Matkowski and J. Okrzesik, On a composite functional equation, Demonstratio Math., 36 (2003), 653–658.

  8. I. Pinelis, Odd-even decomposition of functions, Bull. Aust. Math. Soc., 102 (2020), 104–108.

  9. H. Stetkær, Functional equations on abelian groups with involution, Aequationes Math., 54 (1997), 144–172.

  10. H. Stetkær, Functional equations on abelian groups with involution. II, Aequationes Math., 55 (1998), 227–240.

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Pinelis, I. Characterization of groups of involutions by means of composite functional equations in two variables. Acta Math. Hungar. 165, 287–290 (2021). https://doi.org/10.1007/s10474-021-01191-1

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  • DOI: https://doi.org/10.1007/s10474-021-01191-1

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