[GAP Forum] getting a set of representatives

[Alexander Hulpke]

Dear Gap-Forum,

B. Sahoo asked:

> I want to find a set of representatives of conjugacy classes of  
> involutions
> in a finite group G.

reps:=Filtered(List(ConjugacyClasses(G),Representative),i->Order(i)=2);

Is a brute force method. If your group is very large it will be  
easier to calculate representatives in the 2-Sylow subgroup (or its  
normalizer)

N:=Normalizer(G,SylowSubgroup(G,2));
sreps:=Filtered(List(ConjugacyClasses(N),Representative),i->Order(i)=2);

and then eliminate conjugacy duplicates:

reps:=[];
cl:=[];
for i in sreps do
   if not ForAny(cl,x->i in x) then
     Add(reps,i);
     Add(cl,ConjugacyClass(G,i));
   fi;
od;

and then look at `reps'.

Best,

     Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: hulpke at math.colostate.edu, Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke