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Fields generated by finite rank subgroups of ℚ¯∗
International Journal of Number Theory ( IF 0.5 ) Pub Date : 2020-10-23 , DOI: 10.1142/s1793042121500251 Lukas Pottmeyer 1
International Journal of Number Theory ( IF 0.5 ) Pub Date : 2020-10-23 , DOI: 10.1142/s1793042121500251 Lukas Pottmeyer 1
Affiliation
Let Γ be a finite rank subgroup of ℚ ¯ ∗ . We prove that the multiplicative group of the field generated by all elements in the divisible hull of Γ is free abelian modulo this divisible hull. This proves that a necessary condition for Rémond’s generalized Lehmer conjecture is satisfied.
中文翻译:
由 ℚ¯∗ 的有限秩子群生成的字段
让Γ 是一个有限秩子群ℚ ¯ * . 我们证明了可分外壳中所有元素生成的场的乘法群Γ 是自由阿贝尔模这个可分的船体。这证明了 Rémond 的广义 Lehmer 猜想的一个必要条件得到满足。
更新日期:2020-10-23
中文翻译:
由 ℚ¯∗ 的有限秩子群生成的字段
让