Geodesic
ON THE IDEAL CLASS GROUP OF CERTAIN QUADRATIC FIELDS
Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 575-581

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DOI

Let n(≥ 3) be an odd integer. Let k:= be the imaginary quadratic field and k′:= the real quadratic field. In this paper, we prove that the class number of k is divisible by 3 unconditionally, and the class number of k′ is divisible by 3 if n(≥ 9) is divisible by 3. Moreover, we prove that the 3-rank of the ideal class group of k is at least 2 if n(≥ 9) is divisible by 3.
DOI : 10.1017/S0017089510000431
Mots-clés : 11R11, 11R29 
KISHI, YASUHIRO. ON THE IDEAL CLASS GROUP OF CERTAIN QUADRATIC FIELDS. Glasgow mathematical journal, Tome 52 (2010) no. 3, pp. 575-581. doi: 10.1017/S0017089510000431
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     title = {ON {THE} {IDEAL} {CLASS} {GROUP} {OF} {CERTAIN} {QUADRATIC} {FIELDS}},
     journal = {Glasgow mathematical journal},
     pages = {575--581},
     year = {2010},
     volume = {52},
     number = {3},
     doi = {10.1017/S0017089510000431},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089510000431/}
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