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: [EMAIL PROTECTED], Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
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