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

[M.H.GH]

VP := function( G , p ) 
local P, N, R, Pi, Pj, i, ResultsSet, SizeR, SW; 
P := SylowSubgroup( G , p );
N := Normalizer( G , P );
R := AsList( RightTransversal( G , N ) );
ResultsSet := [];
SizeR := Size( R );
Print ( "\nUpper Bound = Size( RightCosets( G , Normalizer(G,P) ) ) = " , SizeR , " ... \n\n" );
for i in [1..Size( R )] do
Pi := P^R[i];
SW := 1;
for Pj in ResultsSet  do
if Size( Intersection( Pi , Pj ) ) <> 1 then
SW := 0;
continue;
fi;
od;
if SW = 1 then
Add( ResultsSet , Pi );
fi;
od;
Print ( "Result = " , Size( Set( ResultsSet ) ) , " .\n\n");
return Size( Set( ResultsSet ) );
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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