Finite groups with normally embedded subgroups

Zhencai Shen, Shirong Li, Wujie Shi
2010 Journal of group theroy  
A subgroup H of the finite group G is said to be quasinormally (resp. Squasinormally) embedded in G if for every Sylow subgroup P of H, there is a quasinormal (resp. S-quasinormal) subgroup K in G such that P is also a Sylow subgroup of K. Groups with certain quasinormally (resp. S-quasinormally) embedded subgroups of prime-power order are studied. For example, if a group G has a normal subgroup H such that G=H A F and such that for each Sylow subgroup P of H, every member in some M d ðPÞ is
more » ... some M d ðPÞ is quasinormally embedded in G, then G A F: here M d ðPÞ is a set of maximal subgroups of P with intersection the Frattini subgroup.
doi:10.1515/jgt.2010.042 fatcat:nvd4xo55cfdhrnu3cllznfhmk4