On the number of invariant Sylow subgroups under coprime action
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https://doi.org/10.1016/j.jalgebra.2017.07.005 |
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Title
On the number of invariant Sylow subgroups under coprime actionDate
2017-07Publisher
ElsevierBibliographic citation
BELTRÁN, Antonio; SHAO, Changguo. On the number of invariant Sylow subgroups under coprime action. Journal of Algebra, 2017, vol. 490, p. 380-389.Type
info:eu-repo/semantics/articlePublisher version
http://www.sciencedirect.com/science/article/pii/S0021869317303988Version
info:eu-repo/semantics/publishedVersionSubject
Abstract
Let A and G be finite groups such that A acts coprimely on G via automorphisms. We study the number of A-invariant Sylow p-subgroups of G, say V a/p (G), for every prime p, and establish several arithmetical properties ... [+]
Let A and G be finite groups such that A acts coprimely on G via automorphisms. We study the number of A-invariant Sylow p-subgroups of G, say V a/p (G), for every prime p, and establish several arithmetical properties and formulae for these numbers. More precisely, we prove that if G is solvable and H is any A-invariant subgroup of G, then V a/p (H) divides V a/p (G) . [-]
Investigation project
Valencian Government (Proyecto PROMETEOII/2015/011) ; Universitat Jaume I (grant P11B2015-77) ; NNSF of China (No 11301218) and the Natural Science Foundation of Shandong Province (No. ZR2014AM020).Rights
© 2017 Elsevier Inc. All rights reserved.
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