In this paper we attempt to
enlarge classical knot groups K by adding a root to a meridian of K. Thus if K is a
classical knot group with a meridian μ, then the groups we study are of the
form G = K⟨t⟩. This group can always be realized as the group of a
knotted 3-sphere in S5. By using explicit geometric constructions we also
show that such a group G is a 2-knot group and the group of a knot in a
homology 3-sphere. Finally, we show that G is not realizable by any knot in
S3.
