Abstract
AbstractLet
$F_{2^n}$
be the Frobenius group of degree
$2^n$
and of order
$2^n ( 2^n-1)$
with
$n \ge 4$
. We show that if
$K/\mathbb {Q} $
is a Galois extension whose Galois group is isomorphic to
$F_{2^n}$
, then there are
$\dfrac {2^{n-1} +(-1)^n }{3}$
intermediate fields of
$K/\mathbb {Q} $
of degree
$4 (2^n-1)$
such that they are not conjugate over
$\mathbb {Q}$
but arithmetically equivalent over
$\mathbb {Q}$
. We also give an explicit method to construct these arithmetically equivalent fields.
Publisher
Canadian Mathematical Society
Cited by
1 articles.
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1. Arithmetic equivalence under isoclinism;Communications in Algebra;2024-02-09