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Abstract Let G be a finite group, and let π be a set of primes. The aim of this paper is to obtain some results concerning how much information about the π -structure of G can be gathered from the knowledge of the sizes of conjugacy classes of its π -elements and of their multiplicities. Among other results, we prove that this multiset of class sizes determines whether G has a hypercentral Hall π -subgroup.
Víctor Sotomayor (Mon,) studied this question.
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