[GAP Forum] Sylow $p$-subgroups which pairwise intersect trivially

[M.H.GH]

I hope that be useful.

****************

VP := function( G , p ) 

local P, N, R, Pi, Pj, i, j, res, szr, SW; 
P := SylowSubgroup( G , p );
N := Normalizer( G , P );
R := AsList( RightTransversal( G , N ) );
res := [];
szr := Size(R);
Print ( "\nUpper Bound = Size( RightCosets( G , Normalizer(G,P) ) ) = " , szr , " ... \n\n" );
for i in [1..szr] do
Pi := P^R[i];
SW := 1;
for j in [1..szr] do
Pj := P^R[j];
if Size( Intersection( Pi , Pj ) ) <> 1 and i<>j then
SW := 0;
continue;
fi;
od;
if SW = 1 then
Add( res , Pi );
#Print( "|res| = " , Size( Set( res ) ) , " ...  ");
fi;
od;
Print ( "\n\nResult = " , Size( Set( res ) ) , " .\n\n");
return Size( Set( res ) );
end;;

**************



________________________________
 From: zeinab foruzanfar <zeinab_foruzanfar at iust.ac.ir>
To: forum at gap-system.org 
Sent: Monday, April 29, 2013 6:57 PM
Subject: [GAP Forum] (no subject)
 

Hi. I Want some GAP
program to count the number of Sylow $p$-subgroups which pairwise
intersect trivially. Also I want to show that if $P$ and $Q$ are two
Sylow $p$-subgroups, then the intersection of $P^x$ and $P^y$ is trivial
for $x,y \in Q$. Is it possible to send me a program to count these.
Thank you
Best Regards



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