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On the divisibility of the class number of by 16

Published online by Cambridge University Press:  20 January 2009

Philip A. Leonard  and
Kenneth S. Williams
Philip A. Leonard
Affiliation:
Department of Mathematics, Arizona State University, Tempe, Arizona 85287, U.S.A.
Kenneth S. Williams
Affiliation:
Department of Mathematics, and Statistics Carleton University, Ottawa, Ontario, Canada K1S 5B6
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Let d(<0) denote a squarefree integer. The ideal class group of the imaginary quadratic field has a cyclic 2-Sylow subgroup of order ≦8 in precisely the following cases (see for example [5] and [6]):

where p and q denote primes and g, h, u and v are positive integers. The class number of is denoted by h(d) and in the above cases h(d) = 0(mod 8). For cases (i), (ii) and (iii) the authors [6] have given necessary and sufficient conditions for h(d) to be divisible by 16. In this paper we do the same for case (iv) extending the results of Brown [4].

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 26 , Issue 2 , June 1983 , pp. 221 - 231
Copyright
Copyright © Edinburgh Mathematical Society 1983

References

REFERENCES

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