Geodesic
On intersections of solvable Hall subgroups in finite nonsolvable groups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 86-89

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The author continues the investigation of intersections of Hall subgroups in finite groups. Previously, the author proved that in the case when a Hall subgroup is Sylow there are three subgroups conjugate to it such that their intersection coincides with the maximal normal primary subgroup. A similar assertion holds for Hall subgroups in solvable groups. The aim of this paper is to construct examples of a (nonsolvable) group in which the intersection of any four subgroups conjugate to some Hall subgroup is nontrivial. 
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     author = {V. I. Zenkov},
     title = {On intersections of solvable {Hall} subgroups in finite nonsolvable groups},
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     url = {http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a7/}
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V. I. Zenkov. On intersections of solvable Hall subgroups in finite nonsolvable groups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 13 (2007) no. 2, pp. 86-89. http://geodesic.mathdoc.fr/item/TIMM_2007_13_2_a7/