Abstract
Letpbe a prime number andGbe ap-group.6have introduced the notion of a powerfully embedded subgroup ofG. Our main result gives a characterisation of those powerfully embedded subgroups which are contained in the Frattini subgroup ofG, whenpis odd. (Whenp=2, the subgroups characterised have a weaker property than powerful embedding.) This result also yields information on the structure of “d-maximal” 2-groups.
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