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Existence of linear disjointness between an algebraic number field and $p$-cyclotomic field over $ \mathbb{Q}$
Suppose $ K $ be an algebraic number field and $ n $ be an even integer. Is it possible to find atleast one $ p $ such that $ p\equiv 1( \text{mod}~ n)$ and $ \mathbb{Q}(\eta_p) $ is linearly disjoint ...
- 3,054
0
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Not containing $ 2^{i}$-th primitive roots of unity in cyclic galois extension of number field
Suppose $K$ is an algebraic number field. We want to determine whether, for all even $n$, there always exists a cyclic Galois extension $L$ of degree $n$ over $K$ such that the intermediate field $K_2$...
- 2,959