Eight months ago, I submitted a research paper to a good impact factored journal and I got a rejection today. I received the following comment from the reviewer. He suggested that that I submit the paper somewhere else. Also, he stated that there is a hole in the proof of one of my corollaries. He said that the following lemma:
Lemma: Let $r$ be a prime number. Then, for every simple group $S$ with $r \in \pi (S)$, there exists $s \in \pi (S)$ such that $S$ does not possess a Hall $\{r,s\}$-subgroup, where $\pi (S)$ is the set of the prime divisors of $S$.
which I used in the proof of the corollary is not true when $r = 3$ and that $SL(2,7)$ is a counterexample. The above Lemma is already published by some authors in a good journal.
My questions:
1) I checked with gap software and found that indeed $SL(2,7)$ has Hall $\{3,2\}$-subgroup and Hall $\{3,7\}$-subgroup. However, $SL(2,7)$ is not a simple group. Hence it is not a counterexample for the Lemma. Am I right regarding this?
2) I checked my paper and found that, in four out of nine of my results, I have used this lemma by applying it directly in the proof or indirectly by applying another theorem which has used this lemma within its proof. If I pointed this to the editor, is there a chance that he\she may reconsider the status of my paper?