Abstract
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 π of primes, an extension of an arbitrary D π -group by a D π-group is again a D π -group. This result gives a partial answer to Question 3.62 posed by L. A. Shemetkov in the “Kourovka Notebook.”.
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