Existence of normal Hall subgroups by means of orders of products

Antonio Beltrán and Azahara Sáez

Mathematische Nachrichten, 2019, vol. 292, issue 4, 720-723

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.

Date: 2019
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https://doi.org/10.1002/mana.201800165

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