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Article
Peer-Review Record

Some Remarks on the Divisibility of the Class Numbers of Imaginary Quadratic Fields

Mathematics 2022, 10(14), 2488; https://doi.org/10.3390/math10142488
by Kwang-Seob Kim
Reviewer 1:
Reviewer 2: Anonymous
Reviewer 3:
Mathematics 2022, 10(14), 2488; https://doi.org/10.3390/math10142488
Submission received: 8 June 2022 / Revised: 8 July 2022 / Accepted: 10 July 2022 / Published: 17 July 2022

Round 1

Reviewer 1 Report

Major change 

Comments for author File: Comments.pdf

Author Response

The paper has been revised as your recommadation.

Reviewer 2 Report

The paper is devoted to an interesting topic and is technically demanding. The results established seem to be new and could interest mathematicians working on this domain. Of course I must note that this topic belongs in really pure mathematics (rather than applied or interdisciplinary), but it still fits in the scope of the Jounral Mathematics and I thus feel that it would make a nice publication. Therefore, I recommend it for publication.

Author Response

I agree with your opinion.

Reviewer 3 Report

 

Let me describe paper result.  For a given integer $n$, author provide some families of imaginary quadratic number fields whose ideal class group has a subgroup isomorphic to a cyclic group of order $n$.

{\bf Main theorem}. Let $n, q$ be as in main theorem of the paper K. Chakraborty, A. Hoque, Y. Kishi, P.P. Pandey, Divisibility of the class numbers of imaginary quadratic fields. J. Number Theory 185 (2018), 339--348. For each $q$, the class number of $K_{p,2q}$ is divisible by n for all but finitely many $p^ts$. Furthermore, for each $q$ there are infinitely many fields $K_{p,2q}$. 

Author is a serious mathematician, whose papers are published in strong famous and nice journals, including British. The subject is somehow mainstream and result is very good respect to other subject journals and better that usual papers in mathematics. Level is growing. I recommend for publication.  It will be good for journal.

 

 

Author Response

I agree with your opinion.

Round 2

Reviewer 1 Report

Check the numerical calculations again

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