On the converse of Hall's theorem
Chen, Xiaoyu
Original · EN
In this paper, we mainly investigate the converse of a well-known theorem proved by P. Hall, and present detailed characterizations under the various assumptions of the existence of some families of Hall subgroups. In particular, we prove that if p≠ 3 and a finite group G has a Hall {p,q}-subgroup for every prime q≠ p, then G is p-soluble.
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