A Note on Ideal Class Groups

Kenkichi Iwasawa

doi:10.1017/S0027763000012046

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In the first part of the present paper, we shall make some simple observations on the ideal class groups of algebraic number fields, following the group-theoretical method of Tschebotarew. The applications on cyclotomic fields (Theorems 5, 6) may be of some interest. In the last section, we shall give a proof to a theorem of Kummer on the ideal class group of a cyclotomic field.

References

¹⁾ N. Tschebotarew, Zur Gruppentheorie des Klassenkörpers, J reine u. angew. Math., 161 (1929), pp. 179-183.

²⁾ For the classical class field theory used here and in the following, see H. Hasse’s “Klassenkörperbericht” in Jahresbericht D. M.-V., 1926, 1927, 1930.

³⁾ K. Iwasawa, A note on class numbers of algebraic number fields, Abh. Math. Sem. Univ. Hamburg, 20 (1956), pp. 257-258.

⁴⁾ For a more complete result in this direction, see H. Hasse, Über die Klassenzahl abelscher Zahlkòrper, Berlin, 1952, § 37.

⁵⁾ Iwasawa, op. cit.

⁶⁾ Hasse, Klassenzahl, p. 150.

⁷⁾ Hasse, Klassenzahl, p. 152.

⁸⁾ E. Kummer, Über die Irregularität der Determinanten, Monatsber. Akad. d. Wissensch., Berlin, 1853, pp. 194-200.

⁹⁾ Hasse, Klassenzahl, p. 99.

¹⁰⁾ K. Iwasawa, A class number formula for cyclotomic fields, Ann, of Math., 76 (1962), pp. 171-179,

¹¹⁾ Kummer, op. cit.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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A Note on Ideal Class Groups

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