Talk:Sims conjecture

Conjecture statement

@XOR'easter: This article now says:

[ . . . ] if $G$ is a primitive permutation group on a finite set $S$, $G_{\alpha }$ denotes the stabilizer of the point $\alpha$ in $S$, and $d$ is the length of any orbit of $G_{\alpha }$ in the set $S-\{\alpha \}$, then there exists an integer-valued function $f$ such that $|G_{\alpha }|\leq f(d)$.

It seems rather odd to say that "if d is etc. etc. then there exists a function ƒ such that something-about ƒ(d)," because if you say if d is etc. etc. then the exists ƒ, that seems as if which function ƒ is depends on d. Just what the nature of ƒ depends on should be made clear and explicit. Michael Hardy (talk) 17:25, 9 April 2019 (UTC)

I just went ahead and re-ordered pieces of the statement. It should be clearer now, but let me know what you think. — MarkH21 (talk) 18:13, 9 April 2019 (UTC)

The rewrite looks good to me--it is clear what is being defined and what is being proposed. --{{u|Mark viking}} {Talk} 19:33, 9 April 2019 (UTC)

Yes, I think the rewrite is an improvement. Thanks! XOR'easter (talk) 22:36, 9 April 2019 (UTC)

Shouldn't the "there exists f" be before everything else in the statement ?152.77.213.109 (talk) 12:36, 8 December 2021 (UTC)

Ok according to Pyber and Tracey the statemant is (unsurpisingly) that "there exists f such that". Why do they define f on Z is a mystery. Why would one state the result like that is also a mystery to me, as a more user friendly equivalnt version is

"for all ell there exists N such that if G is a primitive permutation group with stabilizers of order larger than N, the non-trivial orbits of the stabilizers have length larger than ell."   

(Sims implies this by taking N = f(ell) -1, and it imples Sims by setting f(ell)= max{ |H| , H has an orbit of size less than ell} ) Well they must have their reasons. But to my eyes, the fact that f is integer valued is irrelevant. 152.77.213.109 (talk) 15:32, 10 December 2021 (UTC)

References