Geodesic
On lattice properties of S-permutably embedded subgroups of finite soluble groups
Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 505-517

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

In this paper we prove the following results. Let π be a set of prime numbers and G a finite π-soluble group. Consider U, V ≤ G and $H\in \mathrm{Hall}_{\pi}(G)$ such that $H\cap V \in \mathrm{Hall}_{\pi}(V)$ and $1\neq H\cap U\in \mathrm{Hall}_{\pi}(U)$. Suppose also $H \cap U$ is a Hall π-sub-group of some S-permutable subgroup of G. Then $H\cap U \cap V\in \mathrm{Hall}_{\pi}(U\cap V)$ and $\langle H\cap U, H\cap V \rangle\in \mathrm{Hall}_{\pi}(\langle U\cap V\rangle)$. Therefore,the set of all S-permutably embedded subgroups of a soluble group G into which a given Hall system Σ reduces is a sublattice of the lattice of all Σ-permutable subgroups of G. Moreover any two subgroups of this sublattice of coprimeorders permute. 
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     author = {Ezquerro, L. M. and G\'omez-Fern\'andez, M. and Soler-Escriv\`a, X.},
     title = {On lattice properties of {S-permutably} embedded subgroups of finite soluble groups},
     journal = {Bollettino della Unione matematica italiana},
     pages = {505--517},
     publisher = {mathdoc},
     volume = {Ser. 8, 8B},
     number = {2},
     year = {2005},
     zbl = {1147.20017},
     mrnumber = {MR2149397},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_2_a13/}
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Ezquerro, L. M.; Gómez-Fernández, M.; Soler-Escrivà, X. On lattice properties of S-permutably embedded subgroups of finite soluble groups. Bollettino della Unione matematica italiana, Série 8, 8B (2005) no. 2, pp. 505-517. http://geodesic.mathdoc.fr/item/BUMI_2005_8_8B_2_a13/