  The exterior degree of a finite group has been introduced in [P. Niroomand
and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39
(2011), 335--343] and the present paper is devoted to study the exterior degree
of infinite groups. We find some inequalities of combinatorial nature, which
generalize those of the finite case and allow us to get structural restrictions
for the whole group.
