Geodesic
Hall subgroups of odd order in finite groups
Algebra i logika, Tome 41 (2002) no. 1, pp. 15-56.

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We complete the description of Hall subgroups of odd order in finite simple groups initiated by F.Gross, and as a consequence, bring to a close the study of odd order Hall subgroups in all finite groups modulo classification of finite simple groups. In addition, it is proved that for every set $\pi$ of primes, an extension of an arbitrary $D_\pi$-group by a $D_\pi$-group is again a $D_\pi$-group. This result gives a partial answer to Question 3.62 posed by L. A. Shemetkov in the “Kourovka Notebook”.
Keywords: finite simple group, Hall subgroup, exceptional groups of Lie type. 
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E. P. Vdovin; D. O. Revin. Hall subgroups of odd order in finite groups. Algebra i logika, Tome 41 (2002) no. 1, pp. 15-56. http://geodesic.mathdoc.fr/item/AL_2002_41_1_a1/

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