Vol. 34, No. 3, 1970

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On S-units almost generated by S-units of subfields

John H. Smith

Vol. 34 (1970), No. 3, 803–805

Let K∕k be a finite galois extension of number fields, S a finite set of primes of K, and Φ a set of intermediate fields. We assume that S and Φ are closed under the action of G(K∕k) and that S contains all the archimedean primes. This paper determines conditions under which the S-units of fields of Φ “almost generate” those of K (i.e., generate a subgroup of finite index).

Mathematical Subject Classification
Primary: 10.65
Received: 10 February 1969
Published: 1 September 1970
John H. Smith