Abstract
For multi-variable extensions of number fields, we study the maximal finite submodules of classical Iwasawa modules. Our principal objects are the unramified Iwasawa modules for two-variable extensions of imaginary quadratic fields. On the one hand, we obtain a novel way to show a certain upper bound, or even the vanishing, of the maximal finite submodules. On the other hand, we obtain a sufficient condition for the non-vanishing, and then construct numerical examples for which the non-vanishing holds.
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