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| Paper IPM / M / 16696 |
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| Abstract: | |
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Investigating on Pólya groups [] in non-Galois number fields, Chabert [] introduced the notion of pre-Pólya group \Po(−)nr, which is a generalization of the pre-Pólya condition, duo to Zantema [].
In this paper, using class field theory, we describe the pre-Pólya group of a Dn-field K, for n ≥ 4 an even integer, where Dn denotes the dihedral group of order 2n. Moreover, for special case n=4, we improve the Zantema's upper bound on the maximum ramification in Pólya D4-fields.
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