Geodesic
The $D_\pi$-property in finite simple groups
Algebra i logika, Tome 47 (2008) no. 3, pp. 364-394

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Let $\pi$ be some set of primes. A finite group is said to possess the $D_\pi$-property if all of its maximal $\pi$-subgroups are conjugate. It is not hard to show that this property is equivalent to satisfaction of the complete analog of Sylow's theorem for Hall $\pi$-subgroups of a group. In the paper, we bring to a close an arithmetic description of finite simple groups with the $D_\pi$-property, for any set $\pi$ of primes. Previously, it was proved that a finite group possesses the $D_\pi$-property iff each composition factor of the group has this property. Therefore, the results obtained mean in fact that the question of whether a given group enjoys the $D_\pi$-property becomes purely arithmetic.
Keywords: finite group, $D_\pi$-property, Sylow theorem. 
@article{AL_2008_47_3_a4,
     author = {D. O. Revin},
     title = {The $D_\pi$-property in finite simple groups},
     journal = {Algebra i logika},
     pages = {364--394},
     publisher = {mathdoc},
     volume = {47},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2008_47_3_a4/}
}
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D. O. Revin. The $D_\pi$-property in finite simple groups. Algebra i logika, Tome 47 (2008) no. 3, pp. 364-394. http://geodesic.mathdoc.fr/item/AL_2008_47_3_a4/