Noether’s Problem for p-Groups with Abelian Normal Subgroups and Central p-Powers
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThe attached file shows areas of improvement.
Comments for author File: 
Comments.pdf
Author Response
Please see the attachment
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsIn this manuscript the authors prove that the field of rational functions $K(G)=K(x(g) : g ∈ G)$ is rational with respect to $K$ if when $G$ is an abelian extension of a cyclic group and $G^p = {g^ p : g ∈ G} ≤ Z(G)$. They also find classification results for this type of groups. The basic result of the paper is represented by Theorem 1.8 with a detailed proof in Section 4, in which Lemma 2.1,Theorems 2.3, 2.4 and Corollary 2.5 play an important role.
Noether problem for AEC-groups (Definition 1.1) is to establish whether $K(G)$ is rational over $K.$
Partial results for this problem have been obtained by Kang, Haeuslein, Hajja and Michailov, the first author of this paper.
In this manuscript, the authors continue the study begun in [Mi1], dropping a certain condition from Theorem 1.7. : $[H(p),\alpha]\subseteq H(p)\cup \{1\}.$
The authors use a faithful $G$- subspace $W$ and show that $W^G$ is rational over $K$. In my opinion, this is an important result, which is presented in the submitted manuscript.
On the other hand, I would recommend the authors to reduce, as much as possible, the percentage of similarity, especially with: info.fmi.shu-bg.net (11%) and with arxiv.org (6%).
I would also recommend a shorter title and I also think that it would be useful to present some examples. A conclusion can also be added.
I recommend the publication of this paper, taking into account, if possible, of these remarks.
Author Response
Comment 1: On the other hand, I would recommend the authors to reduce, as much as possible, the percentage of similarity, especially with: info.fmi.shu-bg.net (11%) and with arxiv.org (6%).
Response 1: I changed the abstract and part of the Introduction. The percentage of similarity comes from Section 3, where are listed a number of Theorems. They are typically used in a large number of articles devoted to Noether’s problem. It is impossible to change anything in them.
Comment 2: I would also recommend a shorter title and I also think that it would be useful to present some examples. A conclusion can also be added.
Response 2: I changed the title and added more explanation and examples to the results in the Introduction.
