Abstract.
A subgroup H of a finite group G is called c-normal in G if there exists a normal subgroup N of G such that G = HN and $H \cap N \leq H_{G} = {\rm core}_{G}(H)$. In this paper, we investigate the class of groups of which every maximal subgroup of its Sylow p-subgroup is c-normal and the class of groups of which some minimal subgroups of its Sylow p-subgroup is c-normal for some prime number p. Some interesting results are obtained and consequently, many known results related to p-nilpotent groups and p-supersolvable groups are generalized.
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Guo, X., Shum, K. On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups. Arch. Math. 80, 561–569 (2003). https://doi.org/10.1007/s00013-003-0810-4
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DOI: https://doi.org/10.1007/s00013-003-0810-4