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