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Archiv der Mathematik

, Volume 110, Issue 5, pp 421–426 | Cite as

On the orders of the non-Frattini elements of a finite group

  • Andrea Lucchini
Article
  • 89 Downloads

Abstract

Let G be a finite group and let \(p_1,\dots ,p_n\) be distinct primes. If G contains an element of order \(p_1 \cdots p_n,\) then there is an element in G which is not contained in the Frattini subgroup of G and whose order is divisible by \(p_1 \cdots p_n.\)

Keywords

Prime graph Non-Frattini elements Non-Frattini prime graph Generating sets. 

Mathematics Subject Classification

20D60 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica “Tullio Levi-Civita”Università degli Studi di PadovaPaduaItaly

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