Existence of normal Hall subgroups by means of orders of products |
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Authors: | Antonio Beltrn Azahara Sez |
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Institution: | Antonio Beltrán,Azahara Sáez |
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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 6 . As a consequence, we also give a π‐decomposability criterion for a finite group also by means of the orders of products. |
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Keywords: | Hall subgroups order of elements p‐nilpotent groups product of elements 20D15 20D20 |
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