Abstract:Let [Formula: see text] be a number field of degree [Formula: see text] over [Formula: see text] and [Formula: see text] its ring of integers. For a prime number [Formula: see text], we determine the types of splittings of [Formula: see text] in [Formula: see text] for which the set [Formula: see text] is of cardinality a power of [Formula: see text]. We prove that this necessary condition is also sufficient for [Formula: see text] to be a subgroup of the additive group [Formula: see text]. Consequently, we sh… Show more
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