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Existence of normal Hall subgroups by means of orders of products

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  • Antonio Beltrán
  • Azahara Sáez

Abstract

Let G be a finite group, let π be a set of primes and let p be a prime. We characterize the existence of a normal Hall π‐subgroup in G in terms of the order of products of certain elements of G. This theorem generalizes a characterization of A. Moretó and the second author by using the orders of products of elements for those groups having a normal Sylow p‐subgroup . As a consequence, we also give a π‐decomposability criterion for a finite group also by means of the orders of products.

Suggested Citation

  • Antonio Beltrán & Azahara Sáez, 2019. "Existence of normal Hall subgroups by means of orders of products," Mathematische Nachrichten, Wiley Blackwell, vol. 292(4), pages 720-723, April.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:4:p:720-723
    DOI: 10.1002/mana.201800165
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