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On a modification of the group of circular units of a real abelian field

✍ Scribed by Bulant, Michal; Kučera, Radan

Book ID
123220453
Publisher
Elsevier Science
Year
2013
Tongue
English
Weight
226 KB
Volume
133
Category
Article
ISSN
0022-314X

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This note deals with a slight change of Sinnott's definition of circular units of an abelian field. The reason for this new definition giving a bigger group of units is as follows. Sinnott's formula for the index of circular units in the full group of units contains two factors which are difficult t

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Let K be a real abelian number field satisfying certain conditions and K n the n th layer of the cyclotomic Z p -extension of K. We study the relation between the p-Sylow subgroup of the ideal class group and that of the unit group module the cyclotomic unit group of K n . We give certain sufficient

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Let k be an imaginary abelian number field whose conductor has at most two distinct prime divisors and whose maximal subfields which are ramified at one prime are imaginary. We shall find a basis for the group C of circular units in k and compute the index of C in the group E of units in k.