On the converse of Hall's theorem

2015/08/02 by Chen, Xiaoyu
#20D10 #20D20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1508.00250

Abstract

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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