Existence of normal Hall subgroups by means of orders of products | Zendy

Beltrán Antonio | Zendy; Sáez Azahara | Zendy

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Existence of normal Hall subgroups by means of orders of products

Author(s) -

Beltrán Antonio,

Sáez Azahara

Publication year - 2019

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201800165

Subject(s) - mathematics , sylow theorems , normal subgroup , order (exchange) , finite group , prime (order theory) , group (periodic table) , characterization (materials science) , pure mathematics , combinatorics , chemistry , materials science , organic chemistry , finance , economics , nanotechnology

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][A. Moretó, ]. 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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