Geodesic
Theorems of Sylow type
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 5, pp. 829-870

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Let $\pi$ be a set of primes. Generalizing the known properties of Sylow subgroups, Hall introduced the classes $E_\pi$, $C_\pi$, and $D_\pi$ of finite groups that contain a Hall $\pi$-subgroup, precisely one conjugacy class of Hall $\pi$-subgroups, and precisely one conjugacy class of maximal $\pi$-subgroups, respectively. The present paper concerns results about $E_\pi$, $C_\pi$, and $D_\pi$ that have been obtained by different authors at different times. Bibliography: 113 titles.
Keywords: Hall subgroup, finite group, finite simple group, Hall property, existence criterion for Hall subgroups, conjugacy criterion for Hall subgroups, finite groups of Lie type, an analogue of Sylow's theorem for Hall subgroups. 
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     author = {E. P. Vdovin and D. O. Revin},
     title = {Theorems of {Sylow} type},
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E. P. Vdovin; D. O. Revin. Theorems of Sylow type. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 66 (2011) no. 5, pp. 829-870. http://geodesic.mathdoc.fr/item/RM_2011_66_5_a0/