Let
K
K
be a finite cyclic extension of the rational number field
Q
Q
, with Galois group
G
(
K
/
Q
)
G(K/Q)
of order
p
a
{p^a}
for an odd prime
p
p
. Armitage and Fröhlich [1] proved that if the order of 2 modulo
p
p
is even and the class number
h
K
{h_K}
of
K
K
is odd then
U
K
+
=
U
K
2
U_K^ + = U_K^2
, where
U
K
{U_K}
is the group of units of the ring of integers
C
K
{\mathcal {C}_K}
of
K
K
,
U
K
+
U_K^ +
is the group of totally positive units, and
U
K
2
U_K^2
is the group of unit squares. The purpose of this paper is to provide a generalization of this result to a larger class of abelian extensions of
Q
.
2
{Q.^2}