Let be a class of groups and a finite group. A chief factor of is called -central in provided . A normal subgroup of is said to be -hypercentral in if every chief factor of below of order divisible by at least one prime in is -central in . The -hypercentre of is the product of all the normal -hypercentral subgroups of . In this paper, we study the structure of finite groups by using the notion of -hypercentre. New characterizations of some classes of finite groups are obtained.
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Li Zhang, Xiaoyu Chen, Wenbin Guo, On -supplemented subgroups of a finite group. Rend. Sem. Mat. Univ. Padova 136 (2016), pp. 175–189DOI 10.4171/RSMUP/136-12