A FAMILY OF REAL 2(N)-TIC FIELDS

We study the family of polynomials P-n(X;a)=R((X+i)(2n))-a/2(n)T((X+i) (2n)) and determine when P,(X; a), a E Z,is irreducible. The roots are all real and are permuted cyclically by a linear fractional transform ation defined over the real subfield of the 2(n)th cyclotomic field. T he families of fields we obtain are natural extensions of those studie d by M.-N. Gras and Y.-Y. Shen, but in general the present fields are non-Galois for n greater than or equal to 4. From the roots we obtain a set of independent units for the Galois closure that generate an ''a lmost fundamental piece'' of the full group of units. Finally, we disc uss the two examples where our fields are Galois, namely a = +/-2(n) a nd a = +/-2(4).239.