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{title2=$\mathbb Q_3^\times/(\mathbb Q_3^\times)^3$}

The valuation and first principal-unit digit give
$$
\mathbb Q_3^\times/(\mathbb Q_3^\times)^3
\cong\mathbb Z/3\mathbb Z\times\mathbb Z/3\mathbb Z.
$$


Cube-class group of the 3-adic numbers

Past exam of the mathematics course of the University of Cambridge / 2024 / iii / Paper 136 / 1 / a / Solution

Cube-class group of the 3-adic numbers ( $Q_{3}^{\times} / (Q_{3}^{\times})^{3}$ )

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Cube-class group of the 3-adic numbers (Q3×​/(Q3×​)3)

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Cube-class group of the 3-adic numbers ( $Q_{3}^{\times} / (Q_{3}^{\times})^{3}$ )

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