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In 1959, Iwasawa proved that the size of the $p$-part of the class groups of a $\mathbb{Z}_p$-extension grows as a power of $p$ with exponent ${\mu}p^m+{\lambda}\,m+\nu$ for $m$ sufficiently large.

In 1959, Iwasawa proved that the size of the $p$-part of the class groups of a $\mathbb{Z}_p$-extension grows as a power of $p$ with exponent ${\mu}p^m+{\lambda}\,m+\nu$ for $m$ sufficiently large. Broadly, I construct conditions to verify if a given $m$ is indeed sufficiently large.

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    Date Created
    • 2013
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  • Text
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    • Partial requirement for: Ph.D., Arizona State University, 2013
      Note type
      thesis
    • Includes bibliographical references (p. 82-84)
      Note type
      bibliography
    • Field of study: Mathematics

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    by Shawn Michael Elledge

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