Existence of normal Hall subgroups by means of orders of products
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https://doi.org/10.1002/mana.201800165 |
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Title
Existence of normal Hall subgroups by means of orders of productsDate
2018Publisher
Wiley-VCH VerlagISSN
0025-584X; 1522-2616Bibliographic citation
Beltrán A, Sáez A. Existence of normal Hall subgroups by means of orders of products.Mathematische Nachrichten. 2018;1–4.https://doi.org/10.1002/mana.201800165Type
info:eu-repo/semantics/articlePublisher version
https://onlinelibrary.wiley.com/doi/10.1002/mana.201800165Version
info:eu-repo/semantics/publishedVersionSubject
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 ... [+]
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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Mathematische Nachrichten, 2018Investigation project
P11B2015-77 ; MTM2016-76196-P ; BES-2014-068325 ; Prometeo II/2015/011/Generalitat ValencianaRights
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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