 It is called the "p"-adic solenoid and is an example of a solenoid group and of a protorus.The "p"-adic rationals are the direct limit of infinite cyclic subgroups of the rational numbers,
and their dual group can be constructed as the inverse limit of the unit circle group under the repeated map

An element of the "p"-adic solenoid can be represented as an infinite sequence of complex numbers "q"0, "q"1, "q"p, ..., with the properties that each "q"i lies on the unit circle and that, for all "i" > 0, "q"ip = "q"i − 1.The group operation on these elements multiplies any two sequences componentwise.