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A criterion for the parity of the class number of an Abelian field with prime power conductor

Published online by Cambridge University Press:  22 January 2016

Ken-Ichi Yoshino
Ken-Ichi Yoshino*
Affiliation:
Department of Mathematics, Kanazawa Medical University, Uchinada-machi, Ishikawa 920-02, Japan
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Let f be a positive integer such that f ≢ 2 (mod 4). Let h0 be the class number of the maximal real subfield of fth cyclotomic field Q(ζf)- It is interesting to determine when h0 is even. Kummer [11] investigated this problem when f is a prime and showed that if h0 is even, then the relative class number h of the cyclotomic field is even (Satz III). Moreover he gave another necessary condition for h0 to be even (Satz IV). In [7] Hasse gave a necessary and sufficient condition for h to be even (Satz 45).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 145 , March 1997 , pp. 163 - 177
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1997

References

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