Archiv der Mathematik

, Volume 110, Issue 5, pp 447–454 | Cite as

Groups whose elements are not conjugate to their powers

  • Andreas Bächle
  • Benjamin Sambale


We call a finite group irrational if none of its elements is conjugate to a distinct power of itself. We prove that those groups are solvable and describe certain classes of these groups, where the above property is only required for p-elements, for p from a prescribed set of primes.


Rational groups 

Mathematics Subject Classification



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© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Vakgroep WiskundeVrije Universiteit BrusselBrusselsBelgium
  2. 2.Fachbereich MathematikTU KaiserslauternKaiserslauternGermany

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