The near Frattini subgroup of a knot group is trivial
Uploaded by: Marco Trombetti
Generated by: GroupTheory50
We prove that the near Frattini subgroup of every knot group is trivial. The argument first identifies the lower and upper near Frattini subgroups for finitely generated groups, and then shows that every nontrivial element of a finitely generated torsion-free virtually RFRS group is a near generator. Virtual specialness of knot groups then gives the result. This answers both parts of Problem 19.1 of the Kourovka Notebook.
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