Geodesic
On $\boldsymbol{A}_{\boldsymbol{n}} \times \boldsymbol{C}_{\boldsymbol{m}}$-unramified extensions over imaginary quadratic fields
Glasgow mathematical journal, Tome 66 (2024) no. 1, pp. 119-125

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DOI

Let $n$ be an integer congruent to $0$ or $3$ modulo $4$. Under the assumption of the ABC conjecture, we prove that, given any integer $m$ fulfilling only a certain coprimeness condition, there exist infinitely many imaginary quadratic fields having an everywhere unramified Galois extension of group $A_n \times C_m$. The same result is obtained unconditionally in special cases.
DOI : 10.1017/S001708952300037X
Mots-clés : unramified extension, class number, quadratic fields 
Kim, Kwang-Seob; König, Joachim. On $\boldsymbol{A}_{\boldsymbol{n}} \times \boldsymbol{C}_{\boldsymbol{m}}$-unramified extensions over imaginary quadratic fields. Glasgow mathematical journal, Tome 66 (2024) no. 1, pp. 119-125. doi: 10.1017/S001708952300037X
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     title = {On $\boldsymbol{A}_{\boldsymbol{n}} \times \boldsymbol{C}_{\boldsymbol{m}}$-unramified extensions over imaginary quadratic fields},
     journal = {Glasgow mathematical journal},
     pages = {119--125},
     year = {2024},
     volume = {66},
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     doi = {10.1017/S001708952300037X},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S001708952300037X/}
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