Let f be a formation function and G an A-group. It is said that A acts f-hypercentrally on G if A acts f-centrally on every A-composition factor of G. In this paper, groups are investigated by f-hypercentral actions. In particular, some well-known results, including a theorem of Huppert and a theorem of Hall–Higman, are generalized.
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Funding
National Natural Science Foundation of China(11471055)
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