Let
p be an odd prime and
q=pm, where
m is a positive integer. Let
ζq be a
qth primitive root of 1 and
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be the ring of integers in
![]()
. In [I. Gaál, L. Robertson, Power integral bases in prime-power cyclotomic fields, J. Number Theory 120 (2006) 372–384] I. Gaál and L. Robertson show that if
52c4d7"">![]()
, where
![]()
is the class number of
![]()
, then if
![]()
is a generator of
![]()
(in other words
![]()
) either
![]()
is equals to a conjugate of an integer translate of
ζq or
![]()
is an odd integer. In this paper we show that we can remove the hypothesis over
![]()
. In other words we show that if
![]()
is a generator of
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then either
![]()
is a conjugate of an integer translate of
ζq or
![]()
is an odd integer.