10:05 AM
@Zophikel No idea, it's outside my area of expertise. Maybe you should ask that on the main site.

@Zophikel you could also ask in the main chatroom or in the Group Theory chatroom.
Although one trouble with your question is that it is unclear what you mean by a disjoint permutation group. I know what people mean by saying that two permutations are disjoint. But I am not really sure what you mean by saying that a group of permutation is disjoint.
Do you perhaps have some set of permutations which are pairwise disjoint? (I.e., it is not necessarily group, just a set consisting of several permutations.)
In any case I think that it should not be difficult to show that:
a) If $\sigma$, $\tau$ are disjoint permutation and $\phi$ is any permutation, then also $\phi\circ\sigma$ and $\phi\circ\tau$ are disjoint.
b) If $\sigma$, $\tau$ are disjoint permutation and $\phi$ is any permutation, then also $\sigma\circ\phi$ and $\tau\circ\phi$ are disjoint.

2 hours later…
11:58 AM
PALTRY, RABBIT, PORTAL... hard for me to think of longer words. In Finnish LOBBY ART would be a single word, but I don't think it counts :-). Still trying to use all the letter of COMPUTERS, but CUSTOMER is missing the P.

4 hours later…
4:03 PM
15

I think that it might be useful to add somewhere advice about other possibilities how to search. (I am not sure what would be right place, but it would be nice to have it somewhere where new users who are reading through help could notice it.) I think that it is useful to know that apart from t...

I took a look at the proposal and think it is a great idea! It seems either way should work (a dedicated help center article or a link to meta post from /help/searching)
I personally would prefer to create a post on meta with all the recommendations and then add a sentence with the link to it to /help/searching. I think it will help maintain one entry point for all who are interesting in the topic.
Please let me know what do you think!

4:31 PM
in whatever, quid, May 31 at 11:47, by quid
@MartinSleziak thanks. I'll try the escalation process.
@NicolasChabanovsky I will just mention that quid marked this question as back in May. AFAICT, this can be used to signal that some post on meta needs attention from Stack Exchange staff.
Whether quid contact the CMs also in other way, apart from adding the tag, I do not know.
Although now that I noticed that you're a moderator on several sites, it is clear that I am saying thing you're familiar with.
BTW you probably noticed that I have suggested basically the same thing as you said above in my answer: Should we add external searches in some help pages about search? And I have also started the CW-post for this purpose: How to search on this site?
Now I noticed your comment on meta. So I see that you have seen the FAQ-post on searching:
Hi everyone! Could you please tell me what is the community's current stand on this question? As I can see, you have already created a meta post about external search options and there is an answer that contains a paragraph that might be added to the /help/searching. Could you please tell me if I understand you correctly? (Btw, I started a conversation in the chat, please feel free to ping there.) — Nicolas Chabanovsky ♦ 24 mins ago