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Powerful Necessary Conditions for Class Number Problems

✍ Scribed by Stéphane Louboutin

Publisher
John Wiley and Sons
Year
1997
Tongue
English
Weight
610 KB
Volume
183
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

We give a necessary condition for the ideal class group of a CM‐field to be of exponent at most two. This condition enables us to drastically reduce the amount of relative class number computation for determination of the CM ‐ fields of some types (e. g. the imaginary cyclic non ‐quadratic number fields of 2 ‐ power degrees) whose ideal class groups are of exponents at most two. We also give a necessary condition for some quartic non ‐ CM ‐ fields to have class number one.

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