On divisibility of \(h^+\) by the prime 5. (English) Zbl 0827.11071

Let \(p\) and \(l\) be primes such that \(p= 2l+1\equiv 7\pmod 8\). The author proves that if the order \(\pmod l\) of 5 is \((l-1)/2\), then 5 does not divide the class number of the maximal real subfield of the \(p\)th cyclotomic field. In a previous paper [Rocky Mt. J. Math. 24, No. 4, 1467–1473 (1994; Zbl 0821.11053)] he established the same result for the prime 3. The present proof is based on similar ideas.


11R29 Class numbers, class groups, discriminants
11R18 Cyclotomic extensions


Zbl 0821.11053
Full Text: EuDML


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[4] JAKUBEC S.: On divisibility of h+ by the prime 3. Rocky Mountain J. Math. (1992) · Zbl 0821.11053
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