 The index of this subgroup of "real" cyclotomic units (those cyclotomic units in the maximal real subfield) within the full real unit group is equal to the class number of the maximal real subfield of the cyclotomic field.If "n" is the power of a prime, then ζ − 1 is not a unit; however the numbers (ζ − 1)/(ζ − 1) for ("a", "n") = 1, and ±ζ generate the group of cyclotomic units in this case ("n" power of a prime).If "n" is a composite number, the subgroup of cyclotomic units generated by (ζ − 1)/(ζ − 1)with ("a", "n") = 1 is not of finite index in general.