Let
π
\pi
be a finite abelian 2-group and
ω
:
π
→
Z
2
=
{
+
1
,
−
1
}
\omega :\pi \to {Z_2} = \{ + 1, - 1\}
be a nontrivial homomorphism. Under these conditions, we compute the group
W
∗
(
π
,
ω
;
Z
)
{W_ \ast }(\pi ,\omega ;Z)
. We also show that
W
2
(
π
,
ω
;
Z
)
{W_2}(\pi ,\omega ;Z)
is isomorphic to
W
2
(
π
,
ω
;
Z
[
1
2
]
)
{W_2}\left ( {\pi ,\omega ;Z\left [ {\frac {1}{2}} \right ]} \right )
.