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New bounds for numbers of primes in element orders of finite groups

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  • Chiara Bellotti
  • Thomas Michael Keller
  • Timothy S. Trudgian

Abstract

Let ρ(n)$\rho (n)$ denote the maximal number of different primes that may occur in the order of a finite solvable group G, all elements of which have orders divisible by at most n distinct primes. We show that ρ(n)≤5n$\rho (n)\le 5n$ for all n≥1$n\ge 1$. As an application, we improve on a recent bound by Hung and Yang for arbitrary finite groups.

Suggested Citation

  • Chiara Bellotti & Thomas Michael Keller & Timothy S. Trudgian, 2023. "New bounds for numbers of primes in element orders of finite groups," Mathematische Nachrichten, Wiley Blackwell, vol. 296(11), pages 5227-5231, November.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:11:p:5227-5231
    DOI: 10.1002/mana.202200484
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