, Volume 41, Issue 1, pp 8-29

Hall Subgroups of Odd Order in Finite Groups

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

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.”.