Abstract
Let G be an arbitrary group. For any nontrivial bicyclic unit u ∈
G, a necessary and sufficient condition for which the pair {u, uf
} generates a nonabelian free group is given. Moreover, it is proved that the above pair always generates a torsionfree subgroup of the unit group U(
G) and the structure of this subgroup ⟨u, uf
⟩ is characterized.
ACKNOWLEDGMENT
This research was supported in part by grant from the Natural Sciences and Engineering Research Council of Canada.