Geodesic
On the heritability of the property $D_\pi$ by subgroups
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 44-52
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For some set of primes $\pi$, a subgroup $H$ of a finite group $G$ is called a $\pi$-Hall subgroup if all prime divisors of $|H|$ are in $\pi$ and $|G:H|$ has no prime divisors from $\pi$. A group $G$ is said to possess the property $D_\pi$ if it has only one class of conjugate maximal $\pi$-subgroups or, equivalently, the complete analog of Sylow's theorem for Hall $\pi$-subgroups is valid in $G$. We investigate which subgroups of $D_\pi$-groups inherit the property $D_\pi$.
Keywords: Hall subgroup, property $D_\pi$, finite simple group, Sylow's theorem. 
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E. P. Vdovin; N. Ch. Manzaeva; D. O. Revin. On the heritability of the property $D_\pi$ by subgroups. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 44-52. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a3/

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